ABSTRACTS
MONDAY: 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).
TUESDAY: Q-THERMODYNAMICS
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
WEDNESDAY: SYMPOSIUM Q-DISSIPATION
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)
COLLOQUIUM
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.
THURSDAY: Q-COMPUTATION
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.
FRIDAY: RELAXATION AND DEPHASING IN Q-SYSTEMS
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.
SATURDAY: Q-THERMODYNAMICS II
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.
POSTERS:
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 s_{z(i)}
s_{z (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 s_{z} , 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
s_{y(i)} s_{y(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-T_{c} 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.