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## Universal Themes of Bose-Einstein Condensation |

“Quantum
Turbulence in Bose-Einstein Condensates” Weakly
interacting, dilute atomic Bose-Einstein condensates (BECs) have proved to be
an attractive context for the study of nonlinear dynamics and quantum effects at
the macroscopic scale. Recently, atomic BECs have been used to investigate
quantum turbulence both experimentally and theoretically, stimulated largely by
the high degree of control which is available within these quantum gases. I shall motivate the use of atomic BECs for
the study of quantum turbulence and distinguish three stages of turbulence -
its generation, its steady state and its decay - and highlight some fundamental
questions regarding our understanding in each of these regimes. Focusing
finally on the decay of the turbulence, I will discuss the use of vortex length
to characterise this regime and show preliminary findings on the effect of
finite temperature on this decay. The
system is modelled using the Zaremba-Nikuni-Griffin scheme [1], whereby the
condensate is described by a dissipative Gross-Pitaevskii Equation, which is
coupled to a quantum Boltzmann equation for the thermal cloud. [1]
E. Zaremba, T. Nikuni, and A. Griffin, JLTP 116, 277 (1999). ---
“Superfluidity
of nucleons and quarks: from nuclei to neutron stars and color superconductors” This
talk will review superfluidity in nuclei and neutron stars, and proposed
pairing states in color superconducting quark matter. Neutron
stars are expected to contain BCS superfluids of paired neutrons, as well as
paired protons in the interior. High
density quark matter, as should be present in the inner cores of neutron stars,
can be paired in a variety of states. As
will be discussed, such quark matter should exhibit strong analogies with the
BEC-BCS crossover in ultracold gases of fermions. ---
“Finite
temperature modelling in superfluid helium” The
vortex tangle dynamics and turbulence in superfluid helium exhibit a strong
dependence on temperature. The Landau two fuid model is the most successful
hydrodynamical theory of superfuid helium, but by the nature of scale separations can not give an adequate description of the processes
involving vortex dynamics and interactions. In my talk I suggest to use the classical
field methods together with a generalised NLS models that incorporate the
correct equation of state and nonlocality of interactions. I will
illustrate the idea by
applying the classical field method to study the behaviour of vortex rings
during expansion and contraction following change in applied pressure. ---
“Lasers and BEC: two variants of the same
phase transition?” In
this talk, I will try to give my personal view on the analogies and differences
between textbook BEC of material particles, laser operation and those
intermediate cases (in particular exciton-polariton BEC and photon BEC) that
have attracted much interest in recent years. Attempts to develop a unitary
theory of all these phenomena will be critically discussed and the most
exciting open problems will be pointed out. ---
“Strongly
interacting Bose gas and quantum dynamics with *ultracold atoms in reduced
dimensions” We
prepare and study strongly interacting two-dimensional Bose gases with dimensionless
gas parameter as high as g=2.8 by Feshbach tuning and by loading the sample
into an optical lattice In the superfluid and BKT transition regimes,
significant down-shifts from the mean-field and perturbation calculations are
observed when g approaches or exceeds one. In the BKT and the quantum critical
regimes, all measured thermodynamic quantities show logarithmic dependence on
the interaction strength. We also outline a prototypical approach to
investigate quantum transport phenomena and quantum quenches. Starting with an
almost pure bosonic superfluid, we
quench the particle interactions and observe an oscillating density fluctuation
in the time and momentum domains.These so called /Sakharov oscillations/,
typically discussed in the context of early universe evolution, provide a
common basis to understand the quantum quench dynamics of atomic superfluid and
the anisotropy of the cosmic microwave background radiation. ---
“Optical
Flux Lattices for Cold Atomic Gases” One
of the most important techniques in the ultracold atom toolbox is the optical
lattice: a periodic scalar potential formed from standing waves of light. Optical lattices are central to the use of
atomic gases to explore strong-correlation phenomena related to condensed matter
systems. I shall describe a novel
form of optical lattice -- a so-called
``optical flux lattice'' -- in which optically dressed atoms experience an
effective magnetic field with high mean density. Optical flux lattices have
narrow energy bands with nonzero Chern numbers, analogous to the Landau levels
of a charged particle in a uniform magnetic field. These lattices will greatly
facilitate the achievement of the quantum Hall regime for ultracold atomic
gases. ---
“Nonequilibrium
superfluidity and internal convection in finite temperature Bose gases” Classical-field
methods provide powerful tools for the non-perturbative simulation of weakly
interacting Bose systems at finite temperatures, in both equilibrium and
non-equilibrium regimes [1]. Here we
study a degenerate Bose gas coupled to two spatially separated heat reservoirs
held at different temperatures, and simulate the onset of heat transport and
superfluid internal convection [2]. We consider the prospects for observing
thermal-superfluid counterflow turbulence in this system. (Lukas Gilz, Tod M.
Wright, James R. Anglin) [1]
P. B. Blakie, A. S. Bradley, M. J. Davis, R. J. Ballagh, and C. W. Gardiner,
Advances in Physics 57, 363 (2008); M.
J. Davis, T. M. Wright, P. B. Blakie, A. S. Bradley, R. J. Ballagh, and C. W.
Gardiner, arXiv:1206.5470. [2]
Lukas Gilz and James R. Anglin, Phys. Rev. Lett. 107, 090601 (2011). ---
“BEC
of magnons at room temperature and spatio-temporal properties of magnon condensate” Magnons
are the quanta of magnetic excitations in a magnetically ordered media. In
thermal equilibrium, they can be considered as a gas of quasiparticles obeying
the Bose-Einstein statistics with zero chemical potential and a temperature
dependent density. We will discuss the room-temperature kinetics and
thermodynamics of the magnons gas in yttrium iron garnet films driven by a
microwave pumping and investigated by means of the Brillouin light scattering
spectroscopy. We show that the thermalization of the driven gas results in a
quasi-equilibrium state described the Bose-Einstein statistics with a non-zero
chemical potential, the latter being dependent on the pumping power. For high
enough pumping powers Bose-Einstein condensation (BEC) of magnons can be
experimentally achieved at room temperature. Spatio-temporal kinetics of the
BEC-condensate will be discussed in detail. Among others interference of two
condensates, vortices, and propagating waves of the condensate density will be
addressed. ---
“Polariton
condensates, how do they complement atom BECs “ Polariton
condensates may be created both spontaneously through a “standard” phase transition towards a Bose
Einstein condensate,or be resonantly driven with a well-defined Initial
phase, speed And spatial distribution. Thanks to the photonic component of
polaritons, the properties of the quantum fluid may be accessed very directly,
with in particular the possibility of detailed in terferometric studies. This
allows for example to probe the long-range coherence properties of a quantum
fluid with unprecedented ease.This also allows testing superfluid properties
with great precision in space and time .Here, will describe the static and
dynamics of vortices in polariton condensates, obtained with a picosecond time
resolution,in different configurations, with in particular their phase
configuration I will show in particular
the dynamics of spontaneous creation of a vortex as well as the dissociation of
a full vortex into two half vortices will also highlight some of the recent
results obtainedthrough the shaping of the system ,either using nanotechnology
processes or using all optical means or both of them his allows in particular
the study superfluid hydrodynamics of polariton fluids. This work has been
performed at EPFL by a dream team of Postdocs, PhDstudents and collaborators.
Lagoudakis, G.
Nardin, T.Paraiso,G.Grosso,F.Manni, YLéger,S.Trebaol,M.Portella Oberli, F .
Morier-Genoud and the help of our theorists friends V, Savona M. Wouters and T
Liew. The CdTe sample that we have been using has been prepared by Regis André at the Universityof
Grenoble,and we strongly benefited from the long time collaboration with the
group of Le Si Dang. ---
“Magnon
Bose-Einstein condensation via spin-current injection” Spin-wave
excitations (magnons) in magnetic insulators can undergo Bose-Einstein
condensation provided magnetization relaxation is small and magnon-magnon interactions
strong. In this talk I will discuss how a partially-condensed magnon gas in a
magnetic insulator can absorb or emit spin current at an interface with a
paramagnetic metal. In particular, I will discuss the dynamics of the magnon
gas that results from coupling to the metal and show that it is in principle
possible to reach magnon condensation by spin injection. ---
“Black
holes as graviton BECs at the critical point” We
discuss a new quantum theory of a black hole according to which the black hole
is a Bose-Einstein condensate of gravitons. This BEC slowly leaks due to
quantum depletion and losses it's gravitons.
The peculiarity of this condensate is that it is at the critical point
of quantum phase transition, very
similar to some cold atomic systems, but because of the special properties of
gravitational interaction black hole BEC
stays at the critical point all the time, even though the occupation number of
gravitons slowly diminishes. This
picture resolves all the known seeming puzzles of the black hole physics, such
as the information paradox, or negative heat of Hawking radiation. It also
naturally explains why the black hole entropy scales the way Bekenstein
predicted. We shall review these ideas
with a special emphasis on the physical analogies and possible experimental
prospects in creating the black hole type systems in the lab. ---
“Bose-Einstein
condensation in the quantum Hall bilayer” Theory
predicts that the ground state of an electron bilayer, in the quantum Hall
regime with one electron per Landau orbital, is a Bose-Einstein condensate of
interlayer excitons. I will introduce this concept and highlight some key
experimental evidence for this state. I will point out that the measured
current-voltage characteristics of the bilayer are those expected for a
dissipative superfluid state with weakly pinned vortices, closely analogous to
the mixed state of a type-II superconductor. Thus there is very good evidence
for the presence of an equilibrium Bose-Einstein condensate of excitons. The
bilayer condensate shows many of the universal themes of BEC, but there are new
twists in the tale. ---
“Observation
of a photonic Berezinskii-Kosterlitz-Thouless transition” The
Berezinskii-Kosterlitz-Thouless (BKT) transition is a two-dimensional phase
transition in which vortex creation competes with entropy production. Here, we
experimentally demonstrate a photonic BKT transition by observing the 2+1D
propagation of an optical beam in a nonlinear photorefractive crystal. A
random-phase input beam sets up an effective thermodynamics, while
interferometry at the output enables direct identification and counting of
vortices. We show that both the number of vortices produced and the universal
change in correlations agree with theoretical predictions, for both focusing
and defocusing nonlinearity (attractive and repulsive interactions). We also
give evidence for the unbinding of vortex pairs at transition. Non-equilibrium
behavior is discussed, with an emphasis on the competition between condensation
and BKT dynamics. --
“Interfacing
cold atoms and solids” Hybrid
quantum systems, which combine ultra-cold
atoms with solid state devices, have attracted considerable attention in the
last few years. I report on our experimental efforts towards the realization of
such systems based on ultra-cold atoms, superconductors and carbon nanowires. In
our experiments, atomic clouds are trapped by electromagnetic fields near
nanostructured and functionalized surfaces. This
research field of “atom chips” delivered already important insights into
fundamental interactions between atoms and surfaces and opens perspectives
towards the coupling of atomic and solid state degrees of freedoms. In our
experiments, we investigate the quantum interface between atomic clouds and
superconducting devices and the interface between atoms and between mesoscopic
electronic systems, represented by carbon nanowires. ---
“Bose-Einstein
condensation and beyond in magnetic insulators” Localized
spin systems, and in particular dimer systems, provide a fantastic laboratory
to study the interplay between quantum effects and the interaction between
excitations. Magnetic field and temperature allow an excellent control on the
density of excitations and various very efficient probes such as neutrons and
NMR are available. Magnetic
insulators can thus be used as ``quantum simulators'' to tackle with great success
questions that one would normally search in itinerant interacting quantum
systems. In
particular they have provided excellent realizations of Bose-Einstein
condensates [1,2]. They allowed to probe the properties of interacting bosons
in a variety of dimensions, and the critical regimes of quantum phase
transitions in such systems. I
will discuss this physics, and the extensions to other dimensions such as one
dimensional systems, for which magnetic insulators allowed to quantitative
probe for Tomonaga-Luttinger liquid physics (see e.g. [3,4]) or to investigate
the effects of disorder and the physics of such phases as the Bose glass phase
occuring for disordered bosons. [1]
T. Giamarchi and A. Tsvelik, Phys. Rev. B 59 11398 (1999). [2]
T. Giamarchi, C. R\"uegg and O. Tchernyshyov, Nat. Phys. 4 198 (2008). [3]
P. Bouillot et al., Phys. Rev. B 83, 054407 (2011). [4] D. Schmidiger et al., Phys. Rev. Lett. 108, 167201 ---
"The
effects of confinement on coherence and superfluidity in atomic gases" Under
the broad umbrella of this title I will try to cover several topics that have
been dear to me in recent years. First, I will introduce the basic physics of
2D atomic gases, where the interplay of harmonic confinement, interactions, and
the finite sample size leads to an intricate interplay between the
Berezinskii-Kosterlitz-Thouless (BKT) physics and Bose-Einstein condensation
(BEC). Next, I will give an example of an important problem, the interaction
shift of the BEC critical temperature, where even in 3D the harmonic
confinement fundamentally changes the physics and the local density
approximation fails. Motivated by these examples, I will then briefly introduce
our new experiment in which we have achieved BEC in a homogeneous atomic gas.
Finally, time permitting, I will also introduce some recent experiments
performed in ring geometry, where the uniformity and periodicity of the
trapping potential along one direction allow for studies of superfluidity in
the most traditional transport sense. ---
“Superfluidity
and coherence in non-equilibrium condensates” The
great experimental progress in realising and studying polariton condensates has
made it possible to now study experimentally a number of fundemental questions
about the relation between lasing, condensation, coherence and
superfluidity. In my talk, I will
discuss the consequences of finite particle lifetime on two particular examples
of these. I will discuss how superfluid
density can be calculated to remain finite despite particle loss[1], and
discuss how it might be measured. I will
also discuss quasi-long-range coherence in a non-equilibrium condensate as has
been recently measured[2]. [1]
J. Keeling, Phys. Rev. Lett. 107 080402 (2011) [2] G. Roumpos et al, Proc. Natl. Acad. Sci, 109
6467 (2012) ---
“Superfluid
Bose and Fermi gases” The
realization of Bose-Einstein condensation in dilute atomic gases has created a
unique experimental platform to study superfluidity in Bose and Fermi gases.
The control over the atoms and their interactions have allowed studies for weak
and strong interactions. For fermions,
the crossover from Bose-Einstein condensation of strongly bound fermion pairs
to weakly bound Cooper pairs has been explored.
These studies illustrate a new approach to condensed-matter physics
where many-body phenomena are realized in dilute atomic gases. ---
“Multi-Orbital
Condensates in Exciton-Polariton-Lattice Systems” Microcavity
exciton-polaritons are hybrid quantum quasi-particles as admixtures of cavity
photons and quantum-well excitons. The inherent light-matter duality provides
experimental advantages to form coherent condensates at high temperatures (e.g.
4-10 K in GaAs and room temperatures in GaN materials), offering immense
opportunity to investigating hydrodynamic vortex properties, superfluidity, and
low energy quantum state dynamics. Recently, we engineer
exciton-polariton-lattice systems in various artificial periodic potential
geometries: two-dimensional (2D) square, triangular, honeycomb and kagome
lattices, where we explore exotic quantum phase order. We characterize our
devices via micro-photoluminescence measurements in both real and momentum
spaces, which enable us to construct
band structures and access spatial ordering. We observe p- and d-orbital
condensate states, vortex-antivortex phase order, Dirac dispersions, and flat
bands in 2D square, honeycomb, triangular, and kagome lattices respectively. We
envision that the polariton-lattice systems will be promising solid-state
quantum emulators in the quest for better understanding strongly correlated
materials. ---
“The
BEC-BCS crossover:what (if anything) do we fundamentally not understand?” I
raise the question:are there any _conceptual_ questions concerning the BEC-BCS
transition which are at present fundamentally not understood? and reach the conclusion:for the s-wave
case,probably no,but for the p-wave case,at least arguably yes with respect to
at least one fundamental issue,namely the changes (if any) of total angular
momentun across the transition. ---
“Superfluid
Transition and Transport Properties in Two-Dimensional, Disordered Bose Fluids” The
interplay of disorder and interactions in quantum fluids is attracting much
attention at the frontier of condensed matter and ultracold atoms. For
two-dimensional interacting bosons, the quantum phase diagram is largely
debated and still at a conjectural stage. In
this contribution, we report the first ab-initio phase diagram of disordered
and interacting ultra-cold atoms in two dimensions. We demonstrate that,
although the disorder renormalizes the chemical potential in a non-local way,
the critical properties at the superfluid to normal fluid transition are of the
BKT type, even in the strong disorder regime, where the atomic density shows
strong spatial modulations. In addition, we study the conducting properties of
two-dimensional Bose fluid by means of a methodological improvement we hereby
introduce. The resulting insulating phase at large disorder strength is shown
to be well described by a thermally-activated behavior of the Arrhenius type,
indicating the existence of a "bad metal" behavior. ---
“Superfluid
3He in the Zero-Temperature Limit: An
Ideal Medium for Measuring the Energy Content of, and Visualizing in Real Time,
Pure Quantum Turbulence” We
can cool superfluid 3He down to a temperature regime (~80 microK) where the
condensate is essentially pure. Here only about 1 in 108 3He atoms remain
unpaired and do not contribute to the condensate. Paradoxically, this vanishingly tenuous gas
of unpaired atoms provides us with the tools for both measuring the energy
content of the system and for imaging topological defects therein. This allows us access to many properties of
the system. Here we concentrate on just two.
First, we can measure the total energy contained in quantum turbulence
by monitoring bolometrically the increase in temperature as the turbulence
decays. (We believe this is the first
measurement of the total energy in any turbulent system.) Secondly, we can use the unpaired ballistic
quasiparticle excitations as a “light” source to illuminate turbulence which we
can generate to order. By detecting the shadows
thrown we can image the turbulent network (to surprisingly high accuracy) and
are in the process of developing a “vortex video” to look at the spatial and
temporal evolution of custom-generated turbulence in the condensate. D.
I. Bradley, S. N. Fisher, A. M. Guénault, R. P. Haley, G. R. Pickett and V.
Tsepelin ---
“Probing
Non-Equilibrium Dynamics in an isolated Quantum System” Understanding
non-equilibrium dynamics of many-body quantum systems is crucial for many fundamental
and applied physics problems ranging from de-coherence and equilibration to the
development of future quantum technologies such as quantum computers which are
inherently non-equilibrium quantum systems. One of the biggest challenges is
that there is no general approach to characterize the resulting quantum states.
In the last years we developed techniques using the full distribution functions
of a quantum observable, and the full phase correlation functions to study the
relaxation dynamics in one-dimensional quantum systems and to characterize the
underlying many body states. Interfering
two 1 dimensional quantum gases allows to study how the coherence created
between the two many body systems by the splitting process [1] slowly dies by
coupling to the many internal degrees of freedom available [2]. The full
distribution function of the shot to shot variations of the interference
patterns [3,4], especially its higher moments, allows characterizing the
underlying physical processes [5]. Two distinct regimes are clearly visible:
for short length scales the system is characterized by spin diffusion, for long
length scales by spin decay [6]. After a rapid evolution the distributions
approach a steady state which can be characterized by thermal distribution
functions. Interestingly, its (effective) temperature is over five times lower
than the kinetic temperature of the initial system. Our
system, being a weakly-interacting Bosons in one dimension, is nearly
integrable and the dynamics is constrained by constants of motion which leads
to the establishment of a generalized Gibbs ensemble and pre-thermalization. We
therefore interpret our observations as an illustration of the fast relaxation
of a nearly integrable many-body system to a quasi-steady state through
de-phasing. The observation of an effective temperature significant different
from the expected kinetic temperature supports the observation of the
generalized Gibbs state [6]. [1] T. Schumm et al. Nature Physics, 1, 57
(2005). [2] S. Hofferberth et al. Nature 449, 324
(2007). [3] A. Polkovnikov, et al. PNAS 103, 6125
(2006); V. Gritsev, et al., Nature Phys. 2, 705 (2006); [4]
S. Hofferberth et al. Nature Physics 4, 489 (2008); [5]
T. Kitagawa et al., Phys. Rev. Lett. 104, 255302 (2010); NJP, 13
073018 (2011) [6] M. Gring et al., Science 337, 1318
(2012); M. Kuhnert et al. Phys. Rev. Lett 110, 090405 (2013) D.
Adu Smith et al. arXiv:1212.4645 ---
“Bose-Einstein
Condensation of Dark Matter Axions” Axions
are hypothetical particles whose existence would explain why the strong
interactions are invariant under the discrete symmetries P and CP. It
has long been known that axions produced by vacuum realignment during the QCD
phase transition in the early universe form a cold degenerate Bose gas and are
a candidate for the dark matter. More
recently it was found that dark matter axions thermalize through gravitational
self-interactions and form a Bose-Einstein condensate (BEC). On time scales long compared to their
rethermalization time scale, a large fraction of dark matter axions go to the
lowest energy state available to them.
In this behaviour they differ from all other dark matter
candidates. Axions accreting onto a
galactic halo fall in with net overall rotation because almost all go to the
lowest energy available state for given angular momentum. In contrast, the other proposed forms of dark
matter accrete onto galactic halos with an irrotational velocity field. The inner caustics are different in the two
cases. I'll argue that the dark matter
is axions because there is observational evidence for the type of inner caustic
produced by, and only by, an axion BEC. ---
“Polariton
high density states: vortices and solitons” New
physics observed in high density polariton systems in semiconductor
microcavities will be described. Following a general overview, attention will
be focussed on the ubiquitous effects of interactions in determining key
properties of high density polariton states. These will include temporal
coherence, vortices, where contrast with atom systems will be made, and bright
solitons. The conditions for creation and stability of single solitons will be
described, as will the observation of trains of solitons containing up to four
phase correlated solitons, with size and separation determined by the healing
length of the quantum fluid. ---
"Thermalization
and Dissipationless Flow of Long Lifetime Microcavity Polaritons" Many
of the experiments on polaritons have used systems in which the lifetime of the
polaritons is a few picoseconds while the thermalization time is just a bit
shorter than this, perhaps by a factor of 4 or 5. This has led to interesting
theory on the effects of nonequilibrium on BEC. We have recently developed new
systems in which the lifetime of the polaritons is a few hundred picoseconds,
while the thermalization time is about the same as before. This has allowed us
to see new effects, such as dissipationless coherent flow over macroscopic
distances, thermalization in a trap with well-defined temperature, and
condensation in a ring trap (Mexican hat potential). I will present a survey of
these recent results. ---
“Gauge
fields with cold atoms” Here
I present our experimental work synthesizing static gauge fields for ultracold
neutral atoms (bosonic and fermionic alkali atoms). I will discuss this gauge field in the
language of spin-orbit coupling where it consists of an equal sum of Rashba and
Dresselhaus couplings. In experiment, we couple two (or more) internal states
of our alkali atoms with a pair of ``Raman'' lasers and load our degenerate
quantum gas into the resulting adiabatic eigenstates which experience
artificial gauge fields. In
this talk, I will explore how the atomic interaction is changed in the presence
of this optical coupling, both for bosons and fermions. ---
“Superfluidity
of ultracold atomic gases” In
this talk I will review some of the
advances in our understanding of
superfluid phenomena in ultracold atomic gases (both Bose and Fermi gases). Special emphasis will
be given to the implications of the hydrodynamic theory of
superfluids at both zero and finite
temperature, including the behavior of the collective oscillations in the presence of harmonic
trapping and the recent observation of second sound and measurement
of the temperature dependence of the superfluid density. The structure of quantized
vortices, their effects on the dynamic
properties of the gas, the quenching
of the moment of inertia and the occurrence of Josephson-like oscillations
will be also discussed. ---
“Hydrodynamic excitations in a
Bose-Einstein condensate” Quantum hydrodynamics describes
the interactions between a superfluid and a normal fluid, where the evolution
of the system to equilibrium depends on their mutual response. Although quantum
hydrodynamics has been studied extensively in liquid helium, ultra-cold atomic
gases provide a new playground for its study, since the mutual interactions can
be calculated ab initio. One of the drawbacks of ultra-cold gasses is the low
densities, where the system is mostly collisionless. We have achieved large
number condensates in sodium, which behave hydrodynamic even in the thermal
cloud. We have studied hydrodynamic excitations above and below the critical
temperature, like sound, heat conduction and out-of-phase dipole modes, and
compared our results with theoretical models. The results show that the naive picture of frictionless
flow of the superfluid has to be reexamined for trapped, ultra-cold gasses.
“Ultracold
metastable helium atoms for quantum atom optics and metrology” Helium
atoms in the metastable triplet state (20 eV above the singlet ground state)
offer unique possibilities for ultracold atom physics. They
can be detected with high efficiency allowing single-atom detection. This can
be exploited in quantum atom optics experiment such as the Hanbury Brown Twiss
effect, which we measured for both helium-3 (fermion:
antibunching) and helium-4 (boson: bunching). The simple atomic structure of
helium allows highly accurate calculation of molecular potentials as well as
atomic energy levels. Ultracold helium atoms provide almost ideal experimental
circumstances to measure transition frequencies and confront these with QED
calculations. In this presentation I will discuss our recent measurement, in a
BEC as well as a DFG, of the energy difference between the two metastable
states of helium, allowing a stringent test of QED, and, by measuring the
isotope shift between helium-4 and helium-3, a measurement of the nuclear
charge radius difference between the alpha-particle and the helion (helium-3
nucleus). Further improvement of this measurement may contribute to the
solution of the proton-size puzzle, i.e. the observation that the size of the
proton, measured in different branches of physics, disagrees by 7 standard
deviations. ---
“Bose-Einstein
Condensation of Photons and Grandcanonical Condensate Fluctuations” Bose-Einstein
condensation, the macroscopic ground state accumulation of particles with
integer spin (bosons) at low temperature and high density, has been observed in
several physical systems, including cold atomic gases and solid state physics
quasiparticles. However, the most omnipresent Bose gas, blackbody radiation
(radiation in thermal equilibrium with the cavity walls) does not show this
phase transition. The photon number is not conserved when the temperature of
the photon gas is varied (vanishing chemical potential), and at low
temperatures photons disappear in the cavity walls instead of occupying the
cavity ground state. Here I will describe an experiment observing a
Bose-Einstein condensation of photons in a dye-filled optical microcavity [1].
Further, recent experiments investigating the second order coherence of the
condensate will be reported. The results give evidence for Bose-Einstein
condensation under grandcanonical ensemble conditions, as can be understood
from effective particle exchange of condensate photons with dye electronic
excitations. [1]
J. Klaers, J. Schmitt, F. Vewinger, and M. Weitz, Nature 468, 545 (2010). ---
“Contrasting
the classical-field method with the broken-symmetry description of Bose
superfluidity” Traditional
descriptions of partially condensed Bose gases begin with the separation of the
Bose field into condensed and non-condensed components. In such approaches, the condensed part is
represented by a classical object -- the condensate order parameter -- that is
in most cases associated with the concept of spontaneous symmetry
breaking. An alternative computational
approach to describing such systems exploits the fact that highly occupied (but
not necessarily condensed) modes of a quantum Bose field can be accurately
approximated by a classical field. Quantities
such as the condensate and the superfluid density are then determined a
posteriori, from the correlations of multimode classical field trajectories. This talk will outline the classical-field
method and review its advantages and limitations, before describing how
characteristic features of the symmetry-breaking approach appear in
classical-field calculations, and can be used to characterise the superfluid
properties of the system. We will argue,
however, that many of the most interesting regimes of nonequilibrium dynamics
that can be described with classical-field methods are beyond the reach of
methods based upon Bose symmetry breaking. =====
“Two-site
noninteracting Bose Hubbard Hamiltonian: state transfer, surface Bloch
oscillations and supersymmetry” (slide) Max
Planck Institute for the Physics of Complex Systems, 01187, Dresden, Germany We
investigate the tunneling dynamics of bosonic particles between two quantum
wells within the framework of the noninteracting Bose Hubbard Hamiltonian and
we demonstrate a number of intriguing and overlooked features associated with
these models. By projecting the system’s Hamiltonian on Hilbert subspaces
spanning different numbers of boson excitations, we demonstrate that processes
such as coherent transport, state localization and surface Bloch oscillations
can take place in Fock space. Furthermore, we show that Hamiltonian
representations of Fock space manifolds differing by one boson obey discrete
supersymmetry relation. ---
“Vortices
and the Berezinskii-Kosterlitz-Thouless, Transition in 2D Systems with
Competing Order” (slide) We
consider a two-dimensional system with two order parameters, one with O(2)
symmetry and one with O(M), near a point in parameter space where they couple
to become a single O(2 + M) order. While
the O(2) sector supports vortex excitations, these vortices must somehow
disappear as the high symmetry point is approached. We develop a variational
argument which shows that the size of the vortex cores diverges as 1/ ∆
and the Berezinskii-Kosterlitz-Thouless transition temperature of the O(2)
order vanishes as 1/ ln(1/∆), where ∆ denotes the distance from the
high- symmetry point. Our
physical picture is confirmed by a renormalization group analysis which gives
further logarithmic corrections, and demonstrates full symmetry restoration
within the cores. ---
“Quantum
kinetic derivation of the non-Equilibrium Gross-Pitaevskii equation for
micro-cavity poaritons” (slide) The
non-equilibrium Gross-Pitaevskii equation proposed by Wouters and Carossotto
for non-resonantly excited polaritons is derived by means of contour
time-ordered Green functions for bosons.
The rate equation of the exciton reservoir
is derived form the Kadanoff-Baym equation with slowly varying center
coordinates and Fourier transformed relative coordinates for particle-particle and
phonon-assisted scattering between the reservoir and the polariton condensate
field. ---
“Nonthermal
Fixed Points and Superfluid Turbulence in an Ultracold Bose Gas” (slide) Authors:
M. Karl*, B. Nowak and T. Gasenzer Turbulence
appears in situations in which, e.g., an energy flux goes from large to small
scales where finally the energy is dissipated. As a result the distribution of
occupation numbers of excitations follows a power law with a universal critical
exponent. The situation can be described as a nonthermal fixed point of the
dynamical equations. Single-particle
momentum spectra for a dynamically evolving Bose gas are analysed using
semi-classical simulations and quantum-field theoretic methods based on
effective-action techniques. These give information about possible universal
scaling behaviour. The connection of this scaling with the appearance of
topological excitations such as solitons and vortices in one-component gases
and domain walls and spin textures in multi-component systems is discussed. In
addition their relation to those found in a field-theory approach to strong
wave turbulence is discussed. In particular for three dimensional systems, the
concept of nonthermal fixed points and its connection to transport processes in
a turbulent system shows new aspects of the condensation dynamics out of
equilibrium. The results open a view on a possibility to study nonthermal fixed
points and superfluid turbulence in experiment without the necessity of
detecting solitons and vortices in situ. ---
“Conditions
for nonmonotonic vortex interaction in two-band superconductors” (slide) We
describe a semianalytic and a fully numerical approach to the calculation of
intervortex interaction in two-band Ginzburg-Landau theory and find conditions
under which the vortices attract or repel in the short-range and in the
long-range [1]. This variability of behavior is the result of the presence of
multiple length scales in the problem. Due to the similarity of the
Ginzburg-Landau energy functional for superconductors to the Gross-Pitaevskii
one for Bose-Einstein condensates it is likely that similar approach can be
used to analyze the interaction between composite/fractional vortices in
multicomponent Bose-Einstein condensates. [1]
A. Chaves, L. Komendova, M. V. Milosevic, J. S. Andrade Jr., G. A. Farias, and
F. M. Peeters, Phys. Rev. B 83, 214523 (2011). ---
“Rotation
of a Spin-Orbit-Coupled Bose-Einstein Condensate” (slide) Recent
experiments [1] have engineered spin-obit (SO) coupling in a neutral atomic
Bose-Einstein condensate through the dressing of two atomic spin states with a
pair of lasers. This has led to an interest in the application of these
systems, such as for spintronic devices. The addition of rotation to the system
adds non-trivial topological defect effects. We consider a mean-field
description of the rotating spin-1/2 Bose-Einstein condensate with spin-orbit
interactions. Through a Thomas-Fermi approximation and working in the
non-linear sigma model formalism, we are able to determine regimes of different
topological defects and ground state profiles. We back these analytical results
up with a series of numerical simulations on the full Gross-Pitaevskii
equation. In particular, these simulations provide a series of phase diagrams
according to the crucial parameters present in the system: the spin-coupling,
the rotation frequency and the interaction strengths. [1]
Y.-J. Lin, K. Jimenez-Garcia & I. B. Spielman, Spin-orbit-coupled
Bose-Einstein condensates, Nature 471, pp. 83-86 (2011). ---
“BCS-BEC
crossover in a quasi-two-dimensional Fermi gas” (slide) ---
“Stochastic
Modelling of Low-Dimensional Bose Gases” (slide) Due
to the prominent role of phase fluctuations, confined systems in
low-dimensional geometries should best be modelled by a classical field method.
We demonstrate that the stochastic Gross-Pitaevskii equation is an ideal model
for describing low-dimensional ultracold atom experiments. In particular, we
show that it can completely reproduce, in an entirely ab initio manner, a range
of low dimensional experiments, including those discussing phase fluctuations,
density profiles and density fluctuations in weakly-interacting 1d Bose gases
and a study of the universal and scale invariant behaviour of 2d Bose gases. In
all these cases, we propose suitable ways to deal with the cut-off problem of
classical field theory, also implementing for the first time an approach that
guarantees a very specific optimum cut-off choice (to the extent that a
classical field theory with a specific cut-off can reproduce the full quantum
behaviour of the system). While focusing here on the properties of the most
relevant ‘classical’ low-energy part of the spectrum (condensate plus low-lying
modes), the presented approach can in principle be generalized to also account
for dynamics of the high-lying part of the spectrum (via a quantum Boltzmann
equation) and is extendable to non-equilibrium polariton condensates. ---
“Coherence
properties and influence of disorder in 2D Bose gases” (slide) ---
"The
Onset of Phase Coherence in a Nonequilibrium Condensate" Abstract:
Recent experiments with BEC of non-interacting photons coupled to an incoherent
phonon bath have raised questions about how to think about the onset of
conference and superfluidity in BEC systems in general. It has been well
established for some time that a Boltzmann equation which keeps no record of
coherence can model the onset of a sharp peak in momentum space, known as a "quasicondensate".
It is also well established that the Gross-Pitaveskii equation can be used to
evolve an interacting system with "noisy coherence" (a single-valued
wave function, but no long range correlation) to long-distance off-diagonal coherence.
We have recently completed theory on the middle regime between these limits,
namely, the onset of noisy coherence from a quasicondensate. This theory
predicts, in agreement with experiments, that the non-interacting photon system
should become a coherent BEC, but we expect it should have either no
superfluidity, or very low critical velocity. ---
“Probing
polaron physics with impurities in condensates” (slide) Recently
it was shown that the Hamiltonian describing impurity atoms immersed in a
Bose-Einstein can be mapped onto the Fröhlich polaron Hamiltonian, provided the
Bogoliubov approximation is valid. The polaron was introduced in condensed
matter physics where it represents a quasiparticle that consists of an electron
in a polar or ionic lattice, dressed by the lattice deformation. For the
BEC-impurity polaron the role of the electron is played by the impurity and the
phonons are replaced by the Bogoliubov excitations. We apply the Feynman
all-coupling approach to describe the transition between the different coupling
regimes and argue that the polaronic strong-coupling regime, which remains
elusive for the solid state polaron, can be probed by using a Feshbach resonance
[1]. Then, we investigate the dynamic
response properties of the BEC-impurity polaron for which we show that Bragg
spectroscopy is an appropriate experimental probing technique [2]. The
resulting spectra exhibit the typically well-known polaronic features, and in
particular the signature of the Relaxed Excited State (RES). [1]
J. Tempere, W. Casteels, M. K. Oberthaler, S. Knoop, E. Timmermans and J. T.
Devreese, Phys. Rev. B 80, 184504 (2009). [2]
W. Casteels, J. Tempere and J. T. Devreese, Phys. Rev. A 83, 033631 (2011). ---
“Topological
Wigner crystal of half-solitons in a spinor Bose-Einstein condensate" (slide) We
consider a one-dimensional gas of half-solitons in a spinor Bose-Einstein
condensate. We calculate the topological interaction potential between the
half-solitons. Using a kinetic equation
of the Vlasov-Boltzmann type, we model the coupled dynamics of the interacting
solitons. We show that the dynamics of the system in the gaseous phase is
marginally stable and spontaneously evolves towards a Wigner crystal. ---
“Measures
of turbulence in Bose-Einstein condensates” (slide) We
present methods to create and characterize turbulent tangles of vortices in
Bose-Einstein condensates. Motivated by work in classical fluids, we
investigate if techniques that are known to efficiently mix classical fluids,
classified as pseudo-Anosov stirring protocols, also efficiently mix vortices
in trapped atomic condensates. In order to characterise turbulence, we develop
some measures that are experimentally accessible, based on the density and
distributin of vortices in trapped atomic condensates. At scales larger than the vortex core size,
we describe how the momentum spectrum of vortices scales with vortex number. --- [Back] |