Lorentz Center - Hot Topics in Quantum Statistical Physics: q-Thermodynamics, q-Decoherence and q-Motors
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    Hot Topics in Quantum Statistical Physics: q-Thermodynamics, q-Decoherence and q-Motors





Brownian motors in physics and biology

Peter Hänggi

University of Augsburg, Germany

Noise is usually thought of as the enemy of order rather as a constructive influence. For the phenomena of Stochastic Resonance and Brownian Motors (and/or molecular motors) [1,2] random noise plays a beneficial role in enhancing detection and/or facilitating directed transmission of information in absence of biasing forces. Here, I will focus on the possibility to rectify noise so that quantum and classical objects can be directed around on a priori designed routes in biological and physical systems. In doing so, the energy from the haphazard motion of (quantum) Brownian particles is extracted to perform useful work against an external load. This very concept together with first experimental realizations is discussed. Moreover, new applications that involve the electron transfer in molecular bridged metallic leads are presented.

[1] R. D. Astumian and P. Hänggi, Brownian Motors, Physics Today, 55 (11): 33-39 (2002).

[2] P. Reimann and P. Hänggi, Introduction to the Physics of Brownian Motors, Appl. Phys. 75: 169-178 (2002).



Q-Brownian motion in ratchet potentials

Stefan Scheidl

University of Koeln, Germany

We investigate the dynamics of quantum particles in a ratchet potential subject to an ac force field. We develop a perturbative approach for weak ratchet potentials and force fields [1]. Within this approach, we obtain an analytic description of dc current rectification and current reversals. Transport characteristics for

various limiting cases -- such as the classical limit, limit of high or low frequencies, and/or high temperatures -- are derived explicitly. To gain insight into the intricate dependence of the rectified current on the relevant parameters, we identify characteristic scales and obtain the response of the ratchet system in

terms of scaling functions. We pay a special attention to inertial effects and show that they are often relevant, for example, at high temperatures. We find that the high temperature decay of the rectified current follows an algebraic law with a non-trivial exponent, j~T-17/6.

[1] S. Scheidl and V.M. Vinokur, Phys. Rev. B 65, 195305 (2002)



Quantum theory of shuttling instability

Tomas Novotny

Department of  Electronic Structures, Charles University, Prague, Czech Republic

We present a quantum theory for an electromechanical instability in a NEMS device [1], the single-electron shuttle first studied by Gorelik et al. [2]. This device consists of a movable single-electron transistor (SET) and exhibits an electromechanical instability from the tunnelling regime to a shuttle regime in which the SET oscillates and carries an integer number of electrons per a cycle. We demonstrate that the characteristic strong correlation between the oscillator motion and the electron transfer persists even in the quantum regime. The noise generated by various sources (shot and thermal, both having quantum components) is found to be very important for the phenomenon. We identify a cross-over from the tunnelling to the shuttling regime using a phase space formulation in terms of the Wigner function, thus extending the previously found classical results to the quantum domain. We also discovered a new dynamical regime, where the shuttling is driven exclusively by the quantum noise.

[1] T. Novotny, A. Donarini, and A.-P. Jauho, Quantum Shuttle in Phase Space, accepted to Phys. Rev. Lett., (2003).

[2] L. Y. Gorelik et al, Phys. Rev. Lett. 80 (20),  4526 (1998).



Fluxon ratchet dynamics in a 1-D circular array of Josephson Junctions

Ken Segall, Terry P. Orlando and Juan J. Mazo

Massachussets Institute of Technology, Cambridge, USA

We describe the experiments, data and analysis related with our work to realize the ratchet effect in a 1-D, circular array of Josephson junctions.  We have fabricated superconducting Nb-AlOx-Nb arrays with carefully chosen parameters designed to realize a ratchet potential for magnetic fluxons (or “kinks”) trapped in the array.  A ratchet potential can be realized by varying the Josephson critical currents and the cell inductances in an asymmetric way.  With small junctions and low temperatures, fluxons can behave like quantum particles and undergo macroscopic quantum tunneling between cells.  With high-impedance junctions, the dynamics are underdamped and the system has two possible states: a zero-voltage state where the fluxon is pinned in a potential minimum and a finite voltage state where the fluxon moves throughout the array.  A current in the array applies a force to the fluxon, eventually causing a transition from the zero voltage state to the running state.  Measurements of the critical force required to move the fluxon, so-called switching current measurements, probe the transport dynamics of the system.  The ratchet potential causes different switching rates in the two different directions.  A temperature-dependent crossover in the average switching current is observed, a possible indication of the onset of quantum tunneling and hence the rectification of quantum fluctuations.  We discuss our device design, experimental setup and results, and analysis and interpretation of the crossover.



Few-bands quantum ratchets
Joël Peguiron, Johannes B. Majer, Milena Grifoni, and Hans Mooij

Delft University, The Netherlands

In the first part of the talk  we investigate theoretically [1] the rectification of quantum fluctuations by unbiased  driving forces in periodic ratchet potentials sustaining few bands below the barrier. Upon restricting the dynamics to the lowest M bands, the total system-plus-bath Hamiltonian ismapped onto a discrete tight-binding model containing all the information on the intra-well as well as the inter-well tunneling motion. A closed form for the current in the incoherent tunneling regime is obtained. We find that in effective single band ratchets no rectification occurs.

In the second part of the talk we report on the measured quantum ratchet effect for vortices in a quasi one-dimensional Josephson junction array [2]. In this solid state device the shape of the vortex potential energy, and consequently the band structure, can be accurately designed. We find that asymmetric structures possessing only one band below the barrier do not exhibit current rectification at low temperatures and low bias currents. The quantum nature of transport is also revealed in universal/non-universal power-law dependence of the measured voltage-current characteristic for samples without/with rectification.

A complete theoretical understanding of our data is missing.

[1] M. Grifoni, M.S. Ferreira, J. Peguiron and J.B. Majer, Phys. Rev. Lett. 89, 146801 (2002).

[2] J.B. Majer, J. Peguiron, M. Grifoni, M. Tuesveld and J.E. Mooij, Phys. Rev. Lett. 90, 056802 (2003).




Energy fluctuations, persistent current and entanglement in the ground state of a system coupled to a bath

Markus Buttiker

University of Geneva, Switzerland

It is often stated that in the ground state a system can not exchange energy with a bath since neither the system nor the bath can give up energy. In this talk we focus on simple model problems which permit an exact discussion of their ground state properties. As a physical illustration we consider a mesoscopic ring with an in-line quantum dot, penetrated by an Aharonov-Bohm flux [1] and capacitatively coupled to an external resistor. This problem is mapped onto a spin boson problem with a level spacing that depends on the Aharonov-Bohm flux. We find that the persistent current decreases and its relative fluctuations away from the average increase with increasing coupling to the reservoir [2]. We make a sharp distinction between systems depending on whether or not the system Hamiltonian commutes (or does not commute) with the total Hamiltonian [3]. The distinction is illustrated by considering the energy fluctuations in the ground state of small systems coupled to a bath [3]. We establish connections between the persistent current, energy fluctuations and the degree of entanglement between system and bath.

[1]  M. Buttiker and C. A. Stafford, Phys. Rev. Lett. 76, 495 (1996).

[2]  P. Cedraschi, V. V. Ponomarenko, and M. Buttiker, Phys. Rev. Lett. 84, 346 (2000).

[3]  K. E. Nagaev and M. Buttiker, Europhys. Lett. 58, 475 (2002).



Quantum heat engines in the maximum power regime

Tammy Humphrey (1), Heiner Linke (2)

 (1) UNSW Sydney, Australia

 (2) University of Oregon, Eugene, USA

Models of experimental  electron tunneling ratchets  [1] predict that such devices have a certain capability to pump heat, even though at very low efficiency [2]. However, utilizing "energy filters", such as 1D-0D-1D resonant tunneling structures, the transfer of electrons between heat baths can in principle be made reversible, allowing the theoretical construction of quantum Brownian heat engines that operate arbitrarily close to Carnot efficiency [3]. As must be the case, the power goes to zero as Carnot efficiency is approached. It is therefore interesting to ask: What is the efficiency of a quantum Brownian heat engine under conditions when it delivers maximum power [4]?  This question will be explored both for the cases of a heat engine and for its reverse realization, the refrigerator. The results will be compared to those for an endo-reversible classical Carnot engine and for the three-level amplifier, a laser-based quantum heat engine [5].

[1] H.  Linke et al., Science 286, 2314 (1999)

[2] T. E. Humphrey et al., Physica E 11, 281 (2001)

[3] T. E. Humphrey et al., PRL 89, 116801 (2002)

[4] T. E. Humphrey, PhD thesis, unpublished.

[5] H.E.D. Scovil and E.O. Schulz-DuBois, PRL 2, 262 (1959)



Radiative quantum thermodynamics

Marlan O. Scully

Princeton University, USA

We present here a quantum Carnot engine in which the atoms in the heat bath are given a small bit of quantum coherence. The induced quantum coherence becomes vanishingly small in the high-temperature limit at which we operate and the heat bath is essentially thermal. However, the phase Φ, associated with the atomic coherence, provides a new control parameter that can be varied to increase the temperature of the radiation field and to extract work from a single heat bath. The deep physics behind the second law of thermodynamics is not violated; nevertheless, the quantum Carnot engine has certain features that are not possible in a classical engine.

In a related problem we study the situation in which ground state atoms are accelerated through a high Q microwave cavity. Unruh radiation is produced with an intensity which can exceed the intensity of ordinary Unruh acceleration radiation in free space by many orders of magnitude. The cavity field at steady state is described by a thermal density matrix under most conditions. However, under some conditions gain is possible, and when the atoms are injected in a regular fashion, the radiation can be produced in a squeezed state.



Probabilistic arrows of time

Juan MR Parrondo

Univesidad Complutense de Madrid, Spain

We present processes which are not invariant under time reversal, but slightly differ from the irreversible processes usually considered in thermodynamics. The inversion of these new processes can occur with a probability less than one but not negligible, and they involve a microscopic decrease of entropy



Tunneling rates for ferromagnetic junctions

Jens Siewert (1), Giuseppe Falci (2), and Klaus Richter (1)

(1) Institut für Theoretische Physik, Universität Regensburg,  Germany

(2) Dipartimento di Metodologie Fisiche e Chimiche per l'Ingegneria, Universita’ di Catania,  Italy

If a tunneling electron is coupled to some other degree of freedom, this may give rise to a zero-bias anomaly in the current-voltage chararcteristics. A prominent example for this phenomenon is the coupling to the modes of the electromagnetic environment of the circuit via the electron charge, leading to the so-called P(E) theory. Here we investigate whether assisted electron tunneling between itinerant ferromagnets may lead to zero-bias anomalies for ferromagnetic tunnel junctions. We compare our results with  recent experiments.



Integrable generalizations of Jaynes Cummings models with counter-routating terms

Luigi Amico,

Universita` di Catania, Italy


We construct models describing interaction between spin and bosonic degrees of freedom using a quantum inverse scattering procedure. The form of the coupling constants result to be  restricted in such a way that the corresponding Hamiltonians are integrable by construction. For a single bosonic mode interacting  with a spin-S the model we find is a generalization of the Jaynes-Cummings model including "counter-rotating" operators. Using connections with Gaudin models, the approach is described also for the case corresponding to many-spins interacting with certain bosonic bath




Quantum Dissipation and Applications

Amir Caldeira

University of Campinas, Brasil

In this talk it is our intention to present the basic ideas of what is known today as “ Quantum Dissipation” and show  its importance to new problems appearing in different areas of  Physics. We shall approach the problem investigating realistic physical situations where the question of dissipation is really relevant and then identify the concrete problems to be tackled. Some examples are; the dissipative quantum tunnelling, the dissipative coherent tunnelling and the decoherence between wave packets in the classically accessible region of the phase space of the system. Once we have accomplished that, we will introduce several examples of applications of the previously developed techniques to superconductivity, magnetism and optics. The relevance of these questions to problems related to quantum computation will be briefly touched upon.



Superconducting flux qubits

Hans Mooij

Delft University of Technology, The Netherlands

We study a superconducting flux qubit that consists of a small ring with three Joesphson junctions. When biased at about a half flux quantum through the ring it has two quantum states with opposite circulating persistent current. Transitions between these states are induced by resonant microwave signals. With continuous radiation, the level splitting can be determined spectroscopically. From such measurements the occurrence of superpositions of the macroscopic states could be determined. More recently, we studied coherent quantum dynamics of a three-junction flux qubit. Rabi oscillations were observed with periods down to 1 ns over a time up to 500 ns. Two- and three pulse experiments were performed to establish the dephasing time. Also, spectroscopic measurements were performed on two coupled qubits. New experiments are in progress, aimed at a reduction of dephasing and improved fidelity of the readout.



Quantum fluctuation effects in 1D Josephson junction arrays

David Haviland,

Royal Institute of Technology (KTH), Stockholm, Sweden

One dimensional arrays of small capacitance Josephson junctions form an interesting system for the study of quantum fluctuation effects in electronic circuits.  The arrays can be modeled as a transmission line with an impedance that can exceed the quantum resistance.  In this case a Coulomb blockade results, in spite of the large Josephson coupling energy and the low impedance of the environment.  The arrays can be fabricated in a SQUID geometry to allow for tuning of the Josephson coupling energy. Experiments will be described which investigate the Coulomb blockade regime in these arrays, and the use these arrays as a tunable electrodynamic environment for the study of tunneling in a single, small capacitance Josephson junction.



Actively controlling decoherence in quantum systems

Paolo Tombesi,

Universita` di Camerino, Italy

Some methods to control decoherence, by actively acting on the quantum system, proposed in the last years, will be discussed. They are quantum feedback  control, dynamical decoupling and stochastic modulation of system parameters.



Overdamped Josephson junction and duality: Between Coulomb blockade  and macroscopic quantum tunneling

Gert-Ludwig Ingold,

Universität  Augsburg, Germany

For ultrasmall Josephson junctions in the presence of an Ohmic environment,  the so-called P(E)-theory predicts a zero bias anomaly. In particular, for weak environmental resistance, the current should diverge as the external  voltage approaches zero. It turns out, however, that this result applies only at sufficiently high voltages and thus describes only a part of the current-voltage characteristics which exhibits a finite peak as a remnant of the dc Josephson effect. Exploiting results of U. Weiss and others on the duality of an overdamped particle in a periodic potential, a global understanding of the current-voltage characteristics is obtained and it is found that two different physical mechanisms are at work. For sufficiently small external resistance, the transport at low voltages is determined by macroscopic quantum tunneling while the high voltage behavior is dominated by Coulomb blockade. It is proposed that a clear distinction between the two mechanisms and thus a verification of this scenario can be achieved by measuring both flux noise and charge noise.

[1] G.-L. Ingold and H. Grabert, Phys. Rev. Lett. 83, 3721 (1999)

[2] H. Grabert and G.-L. Ingold, Europhys. Lett. 58, 429 (2002)



Modulation of dephasing due to a spin-boson environment

(1) Elisabetta Paladino, (2) Maura Sassetti and  (1) Giuseppe Falci

(1)Universita` di Catania, Italy

(2) Universita` di Genova, Italy

We study the reduced dynamics of a spin (qubit) coupled to a spin-boson environment in the case of pure dephasing. We derive formal exact expressions which can be cast in terms of exact integro-differential master equations. We present results for a spin-boson environment with Ohmic dissipation at finite
temperatures. For the special value of the Ohmic damping strength K=1/2 the reduced dynamics is found in analytic form. For K << 1 we discuss the possibility of modulating the effect of the spin-boson environment on the qubit. In particular we study the effect of the crossover to a slow environment dynamics, which
may be triggered by changing both  the temperature and the system-environment coupling.



Is the dynamics of an open quantum system always linear ?

Peter Talkner, and Karen Fonseca Romero

Universität Augsburg,  Germany

The linearity of the dynamics of an open quantum system generally is thought to be a simple consequence of the well established linearity of the Schroedinger equation for the full system that comprises the considered system interacting with its environment. Combined with the linearity of the partial trace over the full density matrix that gives the reduced density matrix of the considered open system, the linearity of the reduced dynamics appears to follow as a trivial statement. This argument, however, overlooks the fact that in order to apply the unitary dynamics of the total system the knowledge of the state of the total system is required. Hence, at least once in the beginning, when the process is started a density matrix of the full system has to be assigned to each possible initial density matrix of the reduced system. We construct this mapping for one of the simplest possible compound systems under the assumption of an experimentally feasible preparation procedure, and show that in general it is not linear and that, consequently, the dynamics of an open quantum system can generally not be represented by a linear mapping.



Dissipative quantum dynamics simulations

Reinhold Egger

Universität  Düsseldorf, Germany

In this talk I will discuss some ideas related to real-time Monte Carlo simulations for dissipative quantum systems. Two recent applications will be discussed in detail: (1) Low-temperature electron transfer dynamics within a spin-boson description, and (2) the problem of resonant tunneling through a double barrier structure in a nanotube.


Stochastic Liouville-von Neuman equations for non-Markovian  quantum dissipation, decoherence and transport

Jürgen T. Stockburger (1) and Hermann Grabert (2)

(1) Universität Stuttgart, Germany,

 (2) Albert-Ludwigs-Universität,  Freiburg, Germany,

Memory effects inherent in the dynamics of open quantum systems have   so far severely restricted the range of applicable methods other   than perturbation theory. A recent approach using stochastic Liouville-von Neuman (SLN) equations [1] formally eliminates quantum memory   effects by transforming them into correlations of c-number noise forces acting on the open system. This allows the use of equations of motion where Feynman-Vernon path integrals used to be the only known   exact formalism for the reduced dynamics. Using Gaussian identities,   the path integral description is transformed into the elementary linear SLN equation


where x (t) and n(t) are coloured noise forces whose   correlation functions reflect the quantum statistical correlations of   the environment interacting with the open system. Stochastic averaging of samples over the distribution of x (t) and n(t) yields the physical reduced density matrix. Many equivalent stochastic processes   with this property exist; the linear SLN equation can be transformed into the process

where the per-sample expectation value                           

is introduced to yield a process which conserves  trr for each sample. This nonlinear SLN equation shows an evident similarity to classical Langevin-type dynamics, to which it  reduces in the classical limit of vanishing Planck’s constant.    Both equations are separable into   stochastic Schrödinger equations through the ansatz

 for the stochastic sample. The use of equations of motion in numerical computation circumvents   the dynamical sign problem inherent in the Monte-Carlo integration of   real-time path integrals. Algorithms based on SLN equations are   applicable for times far beyond the transient timescales at which path-integral based algorithms break down. Applications to the   dynamics of bound systems as well as transport in periodic structures will be discussed, including numerical results.

[1] J.T.  Stockburger  and H. Grabert, Phys. Rev. Lett., 88, 170407 (2002)




Enhancement of Macroscopic Quantum Tunneling by Landau-Zener Transitions

Hermann Grabert and Joachim Ankerhold

Albert-Ludwigs-Universität Freiburg, Germany

Motivated by recent realizations of qubits with a readout by macroscopic quantum tunneling in a Josephson junction, we study the problem of  barrier penetration in presence of coupling to a spin ½ system. It is shown that when the diabatic potentials for fixed spin intersect in the  barrier region, Landau- -Zener transitions lead to an enhancement of the tunneling rate. The effect of these spin flips in imaginary time is in agreement with experimental observations.




Steering the Quantum State of an Electrical Circuit

G. Ithier, E. Collin, A. Aassime, A. Cottet, D. Vion, P. Joyez, P.F. Orfila,  H. Pothier, C. Urbina, M.H. Devoret and D. Esteve.

Quantronics group, SPEC, CEA-Saclay,  Gif sur Yvette Cedex, France

We have designed, fabricated, and operated a superconducting electrical circuit, the quantronium, that can be i) prepared in any quantum superposition of its two lowest energy eigenstates and ii) measured by projection onto one of these eigenstates. This circuit implements a quantum bit (qubit). It is based on the Cooper pair box [1], a device which combines charging and Josephson effects. In our design [2], the qubit can be decoupled from its measuring circuitry during preparation of a quantum state so that relaxation and random dephasing are minimum. We present experimental results demonstrating quantum coherent driven and free evolutions of the qubit, including spin echoes. Decoherence sources are discussed.

[1] V. Bouchiat et al, Physica-Scripta, 76, 165 (1998).

[2] D.Vion et al, Science 296 (2002).



Quantum Coherence of a Superconducting Flux Qubit

Irinel Chiorescu, Yasunobu Nakamura, Cees Harmans and Hans Mooij

Delft  University of Technology, Delft, The Netherlands

We show that a superconducting flux qubit, consisting of a closed loop  interrupted by three Josephson junctions, behaves according to the laws of quantum mechanics when separated sufficiently from external degrees of  freedom. The two states of such a micron-size superconducting ring contain billions of Cooper pairs. From a ground state in which all the Cooper pairs circulate in one direction, application of resonant microwave pulses can excite the system to a state where all pairs move oppositely, allowing us to have control over the coherent superposition of these two states. Under strong microwave driving it was possible to induce hundreds of coherent oscillations. Moreover, multiple pulses can be used to create quantum operation sequences. With a two-pulse sequence we performed Ramsey interference experiments yielding a decoherence time of about 20 ns whereas the spin-echo time (three-pulse sequence) was measured to be about 30 ns. The qubit readout is done by means of switching-event measurements with an attached SQUID revealing quantum-state oscillations with about 60% efficiency. The SQUID has a hysteretic current-voltage characteristic and is in direct contact with the qubit loop. The mutual coupling is relatively large due to the shared kinetic and geometric inductances of the joint part enhancing the qubit signal. The sample fabrication is done by means of e-beam lithography and metal evaporation using the nanotechnology facilities located in our campus (DIMES, TU Delft).



Single shot readout of the flux-qubit

Kouichi Semba

NTT Basic Research Laboratories, Atsugi-shi, Kanagawa, Japan

 We have succeeded in single shot readout of a superconducting flux-qubit. We adopted a design of Josephson persistent-current qubit which consists of  three Josephson junctions arranged in a superconducting loop made of aluminum [1]. An under-damped dc-SQUID, a quantum detector, is configured outside of the qubit which couples inductively with the qubit. From the spectroscopy measurement, we obtained the qubit energy dispersion with an avoided crossing at flux  bias of p

and also an expected energy separation D of the relevant two quantum levels. The switching current distribution of the SQUID detector obtained by single shot measurement showed clear crossover behavior from the classical Landau-Zener type tunneling to the c-shaped crossing of a quantum system, as we change the samples which have larger D. We have obtained a switching histogram of the SQUID in which two peaks corresponding the ground state and the excited state of the qubit separated clearly within this c-shaped crossing  region [2].

[1] J. E. Mooij et al., Science 285, 1036 (1999).

[2] S. Saito et al., in the proceedings of the MQC2 Conference, Napoli, Kluwer Academic Plenum Publishers 2002.



Noise and decoherence in quantum two-state systems: nonlinear coupling and higher-order effects

Yuriy Makhlin (1,2), Gerd Schoen (1,3) and  Alexander Shnirman (1,4)

(1)           Universität  Karlsruhe, Germany

(2)           Landau Institute for Theoretical Physics, Moscow, Russia

(3)  Forschungszentrum Karlsruhe, Institut für Nanotechnologie, Germany

(3)           Theoretical Division, Los Alamos National Laboratory, USA

Motivated by recent experiments with Josephson-junction circuits we reconsider decoherence effects in quantum two-level systems (TLS). On one hand, the experiments demonstrate the importance of $1/f$ noise, on the other hand, by operating at symmetry points one can suppress noise effects in linear order. We, therefore, analyze noise sources with a variety of power spectra, with linear or quadratic coupling,

which are longitudinal or transverse relative to the eigenbasis of the unperturbed Hamiltonian. Manipulations of the quantum state of the TLS define characteristic time scales. We discuss the consequences for relaxation and dephasing processes.



Dephasing and relaxation in a flux qubit coupled to a noisy detector

 Michael Thorwart (1,2), Elisabetta Paladino  (3),  Milena Grifoni (2)

(1) Universität Düsseldorf, Germany

(2) Delft University  of Technology, The Netherlands            

(3) Dipartimento di Metodologie Fisiche e Chimiche per l'Ingegneria, Universita`di Catania, Italy

We investigate the dynamics of a quantum-mechanical two-level system which is coupled to harmonic oscillator representing the detector. The detector itself is damped due to the interaction with its environment. This model system currently receives considerable interest as it finds an application in experimental realizations of a condensed matter qubit (flux qubit). It is  attractive also because the model can be mapped into a spin-boson problem with a spectral density of the bath having a resonance at the detector frequency. By using the numerically exact technique of the quasi-adiabatic propagator path-integral, we calculate the dynamics of the damped two-level system and investigate the dependence of the dephasing and relaxation rates on the various system parameters. A comparison with the conventional rates for a weak coupling to an Ohmic bath reveals important differences. At low temperatures and weak damping, we develop a three-level approximation to find analytical results for the dephasing rates.  We apply the model to the specific device of the flux qubit coupled to a dc-SQUID which has been realized in the Delft Quantum Transport group lead by J. Mooij.



Engineering decoherence of solid state quantum bits

Frank K. Wilhelm

Ludwig-Maximilians-Universität, München, Germany

In order to realize solid state quantum bits, it is crucial to minimize the decoherence from the coupling to the numerous degrees of freedom of the solid state environment and the outside world. I am going to outline, how to engineer the decoherence properties in different ways, motivated by results of statistical physics and / or quantum information theory. One way is to shape the spectrum of the environment by filtering out the relevant frequencies, which leads to a spin boson model with a structured bath. If more than one bath is present, such in the case of a double quantum dot charge qubit, decoherence is related to an electron flow through the device. We show that the decoherence can be controlled through the voltage between the reservoirs and surprisingly is minimal at a finite voltage, i.e., out of equilibrium. Finally, I exemplify how general ideas on engineering decoherence from quantum information research can be implemented using quantum-statistical methods and will benchmark their effectiveness when applied to realistic models of superconducting quantum bits. Examples will be dynamical decoupling and decoherence-free subspaces. I will show that the requirements of engineering decoherence differ between operation and measurement of a qubit and propose a model that implements detector-dominated measurements with long relaxation times using a spin Boson model with a peaked spectral density.




Nonequilibrium quantum decay, decoherence and noise in quantum impurity problems

Ulrich Weiss

Universität Stuttgart, Germany

In quantum impurity models (QIMs), few or many quantum degrees of freedom are coupled to a field. Prominent representatives are the spin-boson model and the Schmid model. QIMs have attracted a great deal of interest recently, because the underlying physics is nontrivial and the models are manageable technically despite their essentially nonperturbative nature. In addition, they have a multitude of experimental applications, including the Kondo effect, quantum dots, dissipative quantum mechanics, tunneling in quantum wires, nanotubes and fractional quantum Hall devices. In this talk recent progress in understanding nonequilibrium transport, statistical fluctuations, and decoherence in these models - obtained upon combining results from the thermodynamic Bethe ansatz with those of the more rigorous Keldysh approach - is reported. At zero temperature, exact results in analytic form covering the full range from weak to strong tunneling have been found. It is also shown that all the QIMs are closely related and the respective reasons are given.



Quantum electrodynamical fluctuations in the macroscopic phase of a Josephson link

Fernando Sols, Heiner Kohler and Paco Guinea

Universidad Autonoma de Madrid, Spain

We study  the equilibrium dynamics of the relative phase in a Josephson link taking into account the fluctuations of the electrodynamic vacuum. The photons act as a superohmic heat bath on the relative Cooper pair number and thus, indirectly, on the macroscopic phase difference f. This leads to an enhancement of the mean square <f 2> that adds to the spread due to the Coulomb interaction carried by the longitudinal electromagnetic field. We also include the coupling to the electronic degrees of freedom due to quasiparticle tunnelling. The simultaneous inclusion of both the radiation field fluctuations and quasiparticle tunnelling leads to a novel type of particle--bath Hamiltonian in which the particle couples with its position and its momentum to two independent bosonic heat baths. We study the interplay between the two mechanisms in the present context and find interference contributions to the phase quantum fluctuations. We explore the observability of the QED effects discussed here.



Berry phase of non-orthogonal resonances

Robert S. Whitney

Theoretical Physics, University of Oxford,United Kingdom

We investigate the dynamics of the resonances of a system coupled to its environment. The non-Hermitian nature of the system's evolution (once one has traced out the environmental degrees of freedom) means that these resonances need not be orthogonal to each other. We systematically calculate the properties of the resonances of a spin-half weakly coupled to a bath of oscillators (the biased spin-boson model), and show that indeed they are not orthogonal. We then investigate the dynamics of these spin-resonances when the spin-Hamiltonian is (a) static and (b) varied adiabatical slowly. The non-orthogonal nature of the resonances manifests itself clearly in the dynamics of spin-state. In case (b) the spin-resonances exhibit a Berry phase which has a rather complicated geometric interpretation, different from naive expectations.



Berry phase for a spin ½ in a classical fluctutating field

Massimo Palma

Dipartimento di Tecnologie dell'Informazione, Università degli studi di Milano, Crema, Italy

Berry phases and related geometrical phases have received renewed interest in recent years due to several

proposal for their use in the implementation of quantum computing gates. Such interest is motivated by the belief that geometric quantum gates  should exhibit an intrinsic fault tolerance in the presence of external noise. Such belief is based on the heuristic argument that being Berry phases geometrical in their nature, i.e. proportional to the area spanned in parameter space, any fluctuating perturbation of zero average should indeed average out. Although this argument seems convincing to the best of our knowledge it has not been quantitatively probed so far. In particular, although several authors have investigated aspects of Berry phases in the presence of quantum external noise, we are not aware of any in which  the effect of classical noise in a simple model of qubit, namely a spin 1/2 interacting with an external classical field with a fluctuating component has been analyzed. This is precisely the aim of this talk. For such system the effects of classical fluctuations in the control parameter on both geometric and dynamic phases is studied and their impact on dephasing analyzed. We will explicitly show that in the adiabatic limit dephasing is due to fluctuations of the dynamical phase.



Multi-photon absorption observed in a superconducting flux qubit

Shiro Saito(1,5), Hirotaka Tanaka(1,5), Michael Thorwart(1,2,3), Hayato Nakano(1,5),

Masahito Ueda(1,4,5), Kouich Semba(1,5), and Hideaki Takayanagi(1,5)

(1) NTT Basic Research Laboratories, NTT Corporation, Japan

(2) University of  Duesseldorf, Germany

(3) Delft University of Technology, The Netherlands

(4) Department of Physics, Tokyo Institute of Technology, Japan

(5) CREST, Japan Science and Technology Corporation, Japan

We have observed multi-photon absorption peaks and dips in the magnetic-field dependence of switching current in a superconducting flux qubit system. Our qubit consists of an aluminum loop with three Josephson junctions and inductively couples to a dc-SQUID as a switching detector[1]. The Josephson energy of the largest junction in the qubit and the qubit energy splitting at the degeneracy point are 350 GHz and 0.86 GHz, respectively. We have achieved strong coupling between the qubit and an RF control line by using an on-chip strip line. Spectroscopy measurements were performed by applying a continuous microwave to the qubit at fixed frequencies and by sweeping the magnetic fields[2]. We used a triangular wave of 140Hz as a bias current to measure the switching current of the dc-SQUID. Up to three resonant

peaks and dips were observed in the magnetic field dependence of the switching current at fixed microwave frequencies. The width of these multi-photon absorption peaks is described by the Bessel functions derived from real-time path-integral expressions[3]. The peak amplitudes are well explained by a phenomenological model based on the Bloch equation[4].

[1] J. E. Mooij et al., Science 285, 1036 (1999).

[2] C. H. van der Wal et al., Science 290, 773 (2000).

[3] L. Hartmann et al., Phys. Rev. E 61, R4687 (2000).

[4] M. C. Goorden, Master thesis, TU Delft (2002); M. C. Goorden and F. K. Wilhelm, cond-mat/0305467.



Quantum Macroscopic Coherence in Josephson Junction Networks with Non Conventional Architectures

Pasquale Sodano,

Dipartimento di Fisica e Sezione I.N.F.N, Università di Perugina, Italy


We shall focus on the interesting properties emerging in Josephson networks with non-conventional architectures showing, by means of explicit examples, how the network’s topology and geometry may either lead to novel and unexpected coherent phenomena or be responsible for taming de- coherence in quantum Josephson devices. We shall also comment on some network’ s geometries leading to remarkable connections with gauge theories with discrete gauge groups.




Coherent magneto-caloric effect superconductive heat engine process cycle

Peter Keefe

24405 Gratiot Avenue, Eastpointe, Michigan 48021 USA

A quantum motor is proposed in which a mesoscopic (coherence range size) superconductor in a macro-quantum state is closed cycled in magnetic field - temperature space (H-T space), the cycle processes including a magneto-caloric magnetization, a magneto-caloric demagnetization accompanied by the Meissner effect, and a heat influx. The first order adiabatic phase transitions of the magneto-caloric processes occur without the appearance of an intermediate state, resulting in movements of the T coordinate of the superconductor in H-T space. These T coordinate movements involve interaction of the quantum mechanically condensed superelectron regime with the normal regime devoid of collective system interaction, the result being an over-all lowering of the entropy of the superconductor. When these T coordinate movements in H-T space are combined with the Meissner effect which positively moves the H coordinate in H-T space, the net effect is a process cycle, unanticipated by Carnot theoretics, which transforms ambient heat energy into work in a manner consistent with the First Law, but, as a result of the macro-quantum state of the superconductor, inconsistent with traditional formulations of the Second Law.



Measurement and control in classical meso-scale thermodynamics

Ken Sekimoto

University of Strasbourg, France

Small systems require careful consideration of the operation of  measurement and control, even on the scales where the quantum interferences are unimportant. With a recently developed method of meso-scale thermodynamics  ("stochastic energetics"), we will discuss about a kind of complementarity relation of the

free-energy measurement of meso-scale systems, and also about two sources of intrinsic irreversibilities related to the operation of making thermal contact with a heat bath.


Work extraction from mesoscopic systems.
A.E. Allahverdyan

University of Amsterdam, The Netherlands

Thermodynamics teaches that maximal work extractable from a state is governed by its energy and entropy. In mesoscopic physics this bound is usually not reachable. The maximal work extraction compatible with quantum mechanics (``ergotropy'') is derived and related with the property of majorization: states more ordered with respect to it, may provide more work.  Several scenarios of work-extraction are discussed, contrasting the thermodynamical intuition, e.g. states with larger entropy may produce more work.  Work extracted in a closed cycle from a two-temperature mesoscopic system cannot exceed the Carnot bound.



Floquet formalism of quantum pumps.

Sang Wook Kim

Max Planck Institut, Dresden, Germany

A quantum pump is a device that generates a dc current at zero bias potential through cyclic change of system parameters. I would like to present Floquet formalism for quantum pumps, which allows us to explore non-adiabatic as well as adiabatic regimes [1]. The issue of the Pauli blocking factor is discussed during the derivation of the current expression of the quantum pumps in the Floquet formalism [2]. Magnetic field inversion symmetry in quantum pumps with discrete symmetries obtained from Floquet formalism is also presented [3].

[1] S. W. Kim, Phys. Rev. B, 66, 235304 (2002)

[2] S. W. Kim, Phys. Rev. B (in press) [cond-mat/0210485]

[3] S. W. Kim, Phys. Rev. B (in press) [cond-mat/0212409]


Decoherence from chaotic internal dynamics

Sang Wook Kim

Max Planck Institut, Dresden, Germany

I would like to present that the classical-quantum correspondence of center of mass motion in two coupled delta-kicked rotors is enhanced by the entanglement of the center of mass motion to the internal degree of freedom. The observed correspondence can be attributed to the decoherence generated from chaotic internal dynamics with a few degree of freedom.

H.-K. Park and S. W. Kim, Phys. Rev.  67, 060102(R) (2003)



Decoherence and gate performance of coupled solid state qubits

M.J. Storcz and F.K.Wilhelm

Ludwig-Maximilians-Universität,  München,Germany

Solid state quantum bits are promising candidates for the realization of a  scalable quantum computer. However, they are usually strongly limited by decoherence due to the many extra degrees of freedom of a solid state system.  We investigate a system of two solid state qubits that are coupled via type sz(i) sz (j)  of coupling. This kind of setup is typical for pseudospin solid-state quantum bits such as charge or flux systems. We evaluate decoherence properties and gate quality factors

in the presence of a common and two uncorrelated baths coupling to sz  , respectively. We show that at low temperatures, uncorrelated baths do degrade the gate quality more  severely. In particular, we show that in the case of a common bath, optimum gate performance of a CPHASE gate can be reached at very low temperatures, because our type of coupling commutes with the coupling to the decoherence, which makes this type of coupling attractive as compared to previously studied proposals with  sy(i) sy(j)  coupling. Although less pronounced, this advantage also applies to the CNOT gate. For superconducting flux qubits it appears to be relatively easy, to implement a tunable coupling between the qubits, if one uses  tunable Josephson junctions. We evaluate possible coupling strengths and show how much extra decoherence is induced by the subgap conductance of  a switchable junction. In the light of these results, we evaluate several options of using intrinsically shunted junctions and show that based on state-of-the art numbers, Josephson field effect transistors and high-Tc   junctions as p-shifters would be a good option, whereas the use of magnetic junctions as p-shifters severely limits quantum coherence.



Compensation of decoherence from telegraph noise by means of bang-bang control

H. Gutmann, W.M. Kaminsky, S.Lloyd and F.K. Wilhelm

Ludwig-Maximilians-Universität,  München,Germany

With growing success in isolating solid-state qubits from external noise sources, the origins of decoherence inherent of the material start to play a relevant role. One representative example are charged impurities in the disordered substrate or junction material, which produce typical telegraph noise and can hence be modeled as bistable fluctuators [1,2]. In order to demonstrate the possibility of the active suppression of the disturbance from a single fluctuator, we theoretically implement an elementary bang-bang control protocol [3,4]. We simulate numerically the random walk of the qubit state on the Bloch sphere with and without bang-bang compensation scheme and compare it with analytical results we receive by use of appropriate Langevin equations in the long-time limit. Hereby we find out, that the deviation of the pure random walk is scaled down approximatively by the ratio of the bang-bang period and the typical flipping time of the bistable fluctuator.; therefore we expect the bang-bang control working as a high-pass filter on the spectrum of noise sources. This indicates, how the influence of 1/f-noise ubiquitous to the solid state world could be reduced. To describe non perfect bang-bang pulses and evaluate their extra dissipating influence on the qubit we also derive two generic random walk models, which can be solved analytically. So we build a realistic picture, how effective our idealized bang-bang scheme might be in practise and which the technical limitations are for this concept in fighting decoherence generated by material defects.

[1] H. Gassmann, F. Marquardt and C. Bruder, Phys. Rev. E  66, 041111 (2002).

[2] E. Paladino, L. Faoro, G. Falci and R. Fazio, Phys. Rev. Lett. 88, 228304 (2002).

[3] S. Lloyd, Phys. Rev. A 62, 022108 (2000).

[4] S.Lloyd and L.Viola, Phys. Rev. A 65, 010101 (2001).



Enhanced shot noise in resonant tunnelling via interacting localised states

Oleg Youravlev, Yu. V. Nazarov

Dept. of NanoScience, Delft University of Technology, The Netherlands

In a variety of mesoscopic systems shot noise is seen to be suppressed in comparison with its Poisson value. In this work we observe a considerable enhancement of shot noise in the case of resonant tunnelling via localised states. We present a model of correlated transport through two localised states which provides both a qualitative and quantitative description of this effect.



Curie-Weiss model for the quantum measurement process

A.E. Allahverdyan, R. Balian and Th.M. Nieuwenhuizen

University of Amsterdam, The Netherlands


A Hamiltonian model is solved, which satisfies all  requirements for a realistic ideal quantum measurement. The system S is a spin-1/2, whose z-component is measured through coupling with an apparatus A=M+B, consisting of a magnet M formed by a set of N >> 1 spins with quartic infinite-range Ising interactions, and a phonon bath B at temperature T. Initially A is in a metastable paramagnetic phase. The process involves several time-scales. Without being much affected, A first acts on S, whose state collapses in a very brief time. The mechanism differs from the usual decoherence. Soon after its irreversibility is achieved. Finally

the field induced by S on M, which may take two opposite values with probabilities given by Born's  rule, drives A into its up or down ferromagnetic phase. The overall final state involves the expected correlations between the result registered in M and the state of S. The measurement is thus accounted for by standard quantum statistical mechanics and its specific features arise from the macroscopic size of the apparatus.


Stationary entanglement induced by dissipation

S. Nicolosi, A. Napoli, A. Messina

INFM, MIUR and Dipartimento di Scienze Fisiche ed Astronomiche, Palermo, Italy

The exact dynamics of 2 two-level dipole-dipole interacting atoms coupled to a common electromagnetic bath and closely located inside a lossy cavity is reported. Stationary radiation trapping effects are found and very transparently interpreted in the context of our approach. We prove that initially injecting one excitation only in the 2 atoms cavity system, loss mechanisms asymptotically drive the matter sample toward a stationary maximally entangled state. The role played by the closeness of the 2 atoms with respect to such a cooperative behaviour is brought to light and carefully discussed.