Search

The relationship between many-body interactions and dimensionality is integral to numerous emergent quantum phenomena. A striking example is the Bose gas, which upon confinement to one dimension (1D) obeys an infinite set of conservation laws, prohibiting thermalization and constraining dynamics. In our experiment, we demonstrate that such 1D behavior can extend much farther into the dimensional crossover towards 3D than expected. Starting from a weakly interacting Bose gas trapped in a highly elongated potential, we perform a quench to instigate dynamics of a single density mode. Employing the theory of Generalized Hydrodynamics, we identify the dominant relaxation mechanism as the 1D dephasing of the relevant collective excitations of the system, the rapidities. Surprisingly, the dephasing remains dominant even for temperatures far exceeding conventional limits of one-dimensionality where thermalization should occur. We attribute our observations to an emergent Pauli blocking of transverse excitations, caused by the rapidities assuming fermionic statistics, despite the gas being purely bosonic. Thus, our study suggests that 1D physics is less fragile than previously thought, as it can persist even in the presence of significant perturbations. More broadly, by employing the exact Bethe ansatz solutions of the many-body system, we facilitate an interpretation of how the emergent macroscopic behavior arises from the microscopic interactions., 17 pages, 12 figures

We present a detailed analysis of the relaxation dynamics in an extended bosonic Josephson junction. We show that stochastic classical field simulations using Gross-Pitaevskii equations in three spatial dimensions reproduce the main experimental findings of M. Pigneur et al., Phys. Rev. Lett. 120, 173601 (2018). We give an analytic solution describing the short time evolution through multimode dephasing. For longer times, the observed relaxation to a phase locked state is caused by nonlinear dynamics beyond the sine-Gordon model, induced by the longitudinal confinement potential and persisting even at zero temperature. Finally, we analyze different experimentally relevant trapping geometries to mitigate these effects. Our results provide the basis for future experimental implementations aiming to study nonlinear and quantum effects of the relaxation in extended bosonic Josephson junctions., 12 pages, 9 figures, restructured and extended article format

Recent years have enjoyed an overwhelming interest in quantum thermodynamics, a field of research aimed at understanding thermodynamic tasks performed in the quantum regime. Further progress, however, seems to be obstructed by the lack of experimental implementations of thermal machines in which quantum effects play a decisive role. In this work, we introduce a blueprint of quantum field machines, which - once experimentally realized - would fill this gap. Even though the concept of the QFM presented here is very general and can be implemented in any many body quantum system that can be described by a quantum field theory. We provide here a detailed proposal how to realize a quantum machine in one-dimensional ultra-cold atomic gases, which consists of a set of modular operations giving rise to a piston. These can then be coupled sequentially to thermal baths, with the innovation that a quantum field takes up the role of the working fluid. In particular, we propose models for compression on the system to use it as a piston, and coupling to a bath that gives rise to a valve controlling heat flow. These models are derived within Bogoliubov theory, which allows us to study the operational primitives numerically in an efficient way. By composing the numerically modelled operational primitives we design complete quantum thermodynamic cycles that are shown to enable cooling and hence giving rise to a quantum field refrigerator. The active cooling achieved in this way can operate in regimes where existing cooling methods become ineffective. We describe the consequences of operating the machine at the quantum level and give an outlook of how this work serves as a road map to explore open questions in quantum information, quantum thermodynamic and the study of non-Markovian quantum dynamics., Comment: 48 pages, 18 figures, replaced by published version

We demonstrate a source for correlated pairs of atoms characterized by two opposite momenta and two spatial modes forming a Bell state only involving external degrees of freedom. We characterize the state of the emitted atom beams by observing strong number squeezing up to -10 dB in the correlated two-particle modes of emission. We furthermore demonstrate genuine two-particle interference in the normalized second-order correlation function $g^{(2)}$ relative to the emitted atoms., Comment: 6 pages, 3 figures

In an effort to address integrability breaking in cold gas experiments, we extend the integrable hydrodynamics of the 1d Lieb-Liniger model with two additional components representing the population of atoms in the first and second transverse excited states, thus enabling a description of quasi-1d condensates. Collisions between different components are accounted for through the inclusion of a Boltzmann-type collision integral in the hydrodynamic equation. Contrary to standard generalized hydrodynamics, our extended model captures thermalization of the condensate at a rate consistent with experimental observations from a quantum Newton's cradle setup., 23 pages, 13 figures

Heat engines, which cyclically transform heat into work, are ubiquitous in technology. Lasers and masers, which generate a coherent electromagnetic field, may be viewed as heat engines that rely on population inversion or coherence in the active medium. Here we put forward an unconventional paradigm of a remarkably simple electromagnetic heat-powered engine that bears basic differences to any known maser or laser: it does not rely on population inversion or coherence in its two-level working medium. Nor does it require any coherent driving or pump aside from two (hot and cold) baths. Strikingly, the proposed maser, in which the heat exchange between these baths mediated by the working medium amplifies the signal field, can attain the highest possible efficiency even if the signal is incoherent., 8 pages, 3 figures

Quantum systems can be characterized by their correlations. Higher-order (larger than second order) correlations, and the ways in which they can be decomposed into correlations of lower order, provide important information about the system, its structure, its interactions and its complexity. The measurement of such correlation functions is therefore an essential tool for reading, verifying and characterizing quantum simulations. Although higher-order correlation functions are frequently used in theoretical calculations, so far mainly correlations up to second order have been studied experimentally. Here we study a pair of tunnel-coupled one-dimensional atomic superfluids and characterize the corresponding quantum many-body problem by measuring correlation functions. We extract phase correlation functions up to tenth order from interference patterns and analyse whether, and under what conditions, these functions factorize into correlations of lower order. This analysis characterizes the essential features of our system, the relevant quasiparticles, their interactions and topologically distinct vacua. From our data we conclude that in thermal equilibrium our system can be seen as a quantum simulator of the sine-Gordon model, relevant for diverse disciplines ranging from particle physics to condensed matter. The measurement and evaluation of higher-order correlation functions can easily be generalized to other systems and to study correlations of any other observable such as density, spin and magnetization. It therefore represents a general method for analysing quantum many-body systems from experimental data.

We study ultra-cold bosons out of equilibrium in a one-dimensional (1D) setting and probe the breaking of integrability and the resulting relaxation at the onset of the crossover from one to three dimensions. In a quantum Newton's cradle type experiment, we excite the atoms to oscillate and collide in an array of 1D tubes and observe the evolution for up to 4.8 seconds (400 oscillations) with minimal heating and loss. By investigating the dynamics of the longitudinal momentum distribution function and the transverse excitation, we observe and quantify a two-stage relaxation process. In the initial stage single-body dephasing reduces the 1D densities, thus rapidly drives the 1D gas out of the quantum degenerate regime. The momentum distribution function asymptotically approaches the distribution of quasimomenta (rapidities), which are conserved in an integrable system. In the subsequent long time evolution, the 1D gas slowly relaxes towards thermal equilibrium through the collisions with transversely excited atoms. Moreover, we tune the dynamics in the dimensional crossover by initializing the evolution with different imprinted longitudinal momenta (energies). The dynamical evolution towards the relaxed state is quantitatively described by a semiclassical molecular dynamics simulation., SciPost Physics, 9 (4), ISSN:2542-4653

We develop a highly efficient method to numerically simulate thermal fluctuations and correlations in non-relativistic continuous bosonic one-dimensional systems. The method is suitable for arbitrary local interactions as long as the system remains dynamically stable. We start by proving the equivalence of describing the systems through the transfer matrix formalism and a Fokker-Planck equation for a distribution evolving in space. The Fokker-Planck equation is known to be equivalent to a stochastic differential (It\={o}) equation. The latter is very suitable for computer simulations, allowing the calculation of any desired correlation function. As an illustration, we apply our method to the case of two tunnel-coupled quasi-condensates of bosonic atoms. The results are compared to the predictions of the sine-Gordon model for which we develop analytic expressions directly from the transfer matrix formalism., Comment: Version that was accepted by Phys. Rev. A. arXiv admin note: substantial text overlap with arXiv:1712.01190

We propose to implement a quantized thermal machine based on a mixture of two atomic species. One atomic species implements the working medium and the other implements two (cold and hot) baths. We show that such a setup can be employed for the refrigeration of a large bosonic cloud starting above and ending below the condensation threshold. We analyze its operation in a regime conforming to the quantized Otto cycle and discuss the prospects for continuous-cycle operation, addressing the experimental as well as theoretical limitations. Beyond its applicative significance, this setup has a potential for the study of fundamental questions of quantum thermodynamics., Comment: 11 pages, 4 figures; v4: changes in the affiliations and the acknowledgements

We consider the slow light propagation in an atomic medium with a tripod level scheme. We show that the coexistence of two types of dark-state polaritons leads to the propagation dynamics, which is qualitatively different from that in a $\Lambda $-medium, and allows therefore for very efficient conversion of signal photons into spin excitations. This efficiency is shown to be very close to 1 even for very long signal light pulses, which could not be entirely compressed into a Lambda-medium at a comparable strength of the control field., Comment: 7 pages, 3 eps figures, final version published in Phys. Rev. A

The object of investigation is double radiooptic resonance in 87Rb atomic vapor contained in a cell covered by an antirelaxation coating. The Dicke narrowing is studied in terms of the quantum-kinetic approach. It is found that optical pumping using a laser with a “wide” radiation spectrum makes it possible to improve the short-term stability of the frequency standard by an order of magnitude compared with a narrow-spectrum laser.

We have investigated theoretically the formation of a coherent population trapping resonance in a finite-size vapour cell without a buffer gas. We have demonstrated the novel mechanisms of the resonance narrowing: an analogue of the Dicke effect and light-induced narrowing. In the light-induced narrowing regime the parameters of the coherent population trapping resonance weakly depend on the cell size and the type of coating.

We investigate conditions under which multiatom absorption of a single photon leads to cooperative decay. Our analysis reveals the symmetry properties of the multiatom Dicke states underlying the cooperative decay dynamics and their spatio-temporal manifestations, particularly, the forward-directed spontaneous emission investigated by Scully et al (2006 Phys. Rev. Lett. 96 010501).

The results of theoretical and numerical analysis of resonances of coherent population trapping in 87Rb atomic vapors, obtained using copropagated linearly polarized waves, are presented. Various schemes for exciting dark resonance are compared with a view to obtaining a new-generation small-size quantum frequency standard.

We theoretically investigate the free dispersion, scattering and disintegration of an N-particle quantum soliton by Bragg light pulses, comparing the exact quantum result with its quasiclassical (mean-field) limit. Remarkably, we find that the correlation properties of a quantum soliton approach the (mean-field) limit very rapidly as the particle number N grows. A modest discrepancy between the classical and quantum results is observed for N = 3.

We consider adiabatic propagation of a pair of quantized light pulses in a coherently prepared atomic medium with the tripod level configuration. We find that under conditions of electromagnetically induced transparency, two distinct polariton modes are simultaneously formed in the medium. These polaritons, represented by certain coherent superpositions of the quantized fields, have different group velocities; the fast one propagates at essentially the speed of light, while the group velocity of the slow polariton can be dynamically reduced to zero. The state mapping between the electromagnetic field and atomic ensemble is also demonstrated.

Previous theoretical work reviewed in [E.B. Alexandrov et al. Interference of atomic states (Springer, 1993)] has questioned the existence of isotropic quantum beats in atoms. The present work addresses this issue in dedicated experiments involving a pulsed pump-probe detection scheme. The thus obtained results show clear evidence of isotropic quantum beats for which a physical interpretation is given within the coupled-uncoupled state formalism. We suggest that assumptions made in the earlier theoretical work with respect to the structure of the light field make the predictions applicable to scattering only of single photons by atoms and not to scattering of the classical-like light pulses used in ordinary experiments.

We present a brief review of our recent results concerning non-mean-field effects of laser-induced dipole–dipole interactions on static and dynamical properties of atomic Bose–Einstein condensates.

The metal line profiles of different ions observed in high HI column density systems [N(HI) > 10^{16} cm^{-2}] in quasar spectra can be used to constrain the ionization structure and kinematic characteristics of the absorbers. For these purposes, a modified Monte Carlo Inversion (MCI) procedure was applied to the study of three absorption systems in the spectrum of the HDF-South quasar J2233-606 obtained with the UVES spectrograph at the VLT/Kueyen telescope. The MCI does not confirm variations of metal abundances within separate systems which were discussed in the literature. Instead, we found that an assumption of a homogeneous metal content and a unique photoionizing background is sufficient to describe the observed complex metal profiles. It was also found that the linear size L and the line-of-sight velocity dispersion sigma_v measured within the absorbers obey a scaling relation, namely, sigma_v increases with increasing L, and that metal abundance is inversely proportional to the linear size of the system: the highest metallicity was measured in the system with the smallest L., 10 pages, 7 ps figures, accepted to A&A

The structural factors for the single-and double-component Bose-Einstein condensates of neutral atoms in a spherically symmetric harmonic trap are derived. The approach adopted in this paper is applicable in the low excitation energy limit, where the well-known Stringari dispersion relation is valid. Our expression is compared with the quasi-classical one, which is shown to overestimate the structural factor. It is argued that the second component first splits the frequency of collective condensate oscillations, which corresponds to the energy transferred by scattering, into two branches and then multiplies the single-component structural factor by some coefficient that can be greater than unity. The analysis is used to estimate the properties of an experimentally implemented double-component condensate of 87Rb atoms.

The connection between the non-equilibrium dynamics of isolated quantum many-body systems and statistical mechanics is a fundamental open question. It is generally believed that the unitary quantum evolution of a sufficiently complex system leads to an apparent maximum-entropy state that can be described by thermodynamical ensembles. However, conventional ensembles fail to describe the large class of systems that exhibit non-trivial conserved quantities. Instead, generalized ensembles have been predicted to maximize entropy in these systems. In our experiments we explicitly show that a degenerate one-dimensional Bose gas relaxes to a state that can be described by such a generalized ensemble. This is verified through a detailed study of correlation functions up to 10th order. The applicability of the generalized ensemble description for isolated quantum many-body systems points to a natural emergence of classical statistical properties from the microscopic unitary quantum evolution., 5 pages + 4 pages supp. mat., 4 figures

A transformation formula for wave functions of type $$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l}$$ , where ψn is the eigenfunction of a harmonic oscillator for the nth energy level, was found for an arbitrary rotation of the (x 1, x 2) Cartesian system. By way of example, matrix elements for contact interaction of two particles in an external harmonic potential field were calculated.

We present a self-consistent method of taking into account back action of a laser radiation to a Bose-Einstein condensate of neutral atoms. The light is coherently scattered inside the degenerate atomic sample, thus its intensity and, consequently, the atomic ground level AC Stark shift are spatially varying. This leads to a small deformation of the atomic cloud and, if the external radiation is abruptly switched off, to generation of collective excitations.

We present a theory of a resonant laser light propagation through a vapor cell in a case characterized by the two key features: (i) atoms undergo optical pumping into particular sublevels of their ground state, (ii) vapor density is low enough to avoid relaxation of these sublevels caused by interatomic collisions.

We discuss modifications of the kinetic equation for the density matrix of molecular quantum particles. The changes include non-local effects which follow from the assumption of the collapse of wave functions during velocity changing collisions. We present an experimental proposal which represents a test of the new model. A nonlinear medium response caused by action of strong laser light can give new insight into the description of gas kinetics with the quantum theory.

A solution is obtained for the system of Maxwell-Schrodinger equations describing the propagation of a laser pulse through a three-level Λ medium in which the initial atomic populations are in a specially prepared coherent superposition of low-energy states. This solution describes a new type of transparency which is characterized by the presence of conversion of the frequency of the incident pulse and can be used, specifically, to produce “optical keys” and frequency converters for laser radiation.

We experimentally investigate the back-scattering properties of an array of atoms that is evanescently coupled to an optical nanofiber in the strongly non-paraxial regime. We observe that the power and the polarization of the back-scattered light depend on the nanofiber-guided excitation field in a way that significantly deviates from the predictions of a simple model based on two-level atoms and a scalar waveguide. Even though it has been widely used in previous experimental and theoretical studies of waveguide-coupled quantum emitters, this simple model is thus in general not adequate even for a qualitative description of such systems. We develop an ab initio model which includes the multi-level structure of the atoms and the full vectorial properties of the guided field and find very good agreement with our data.

Non-equilibrium dynamics of isolated quantum many-body systems play an important role in many areas of physics. However, a general answer to the question of how these systems relax is still lacking. We experimentally study the dynamics of ultracold one-dimensional (1D) Bose gases. This reveals the existence of a quasi-steady prethermalized state which differs significantly from the thermal equilibrium of the system. Our results demonstrate that the dynamics of non-equilibrium quantum many-body systems is a far richer process than has been assumed in the past.

We present a quantum theory of slow light beyond the weak probe pulse approximation. By reduction of the full Hamiltonian of the system to an effective Hamiltonian for a single quantum field we demonstrate that the concept of dark-state polaritons can be introduced even if the linearized approach is no longer valid. The developed approach allows us to study the evolution of non-classical quantum states of the polariton field., Comment: 9 pages, 4 figures

We derive equations that describe the dynamics of three-level atoms with a cascade system of levels interacting with two resonant coherent fields in conditions where cooperative relaxation dominates over incoherent spontaneous emission. We calculate the temporal dynamics of the values of the atomic populations. The possibility of coherent population trapping in the presence of the cooperative decay is established. Finally, we calculate the averaged population of the intermediate level as a function of detuning for different values of the coupling constant.

We demonstrate that optically excited states of atoms composing a Bose-Einstein condensate can undergo a sufficiently nonexponential decay.

We present an approach to monitoring and controlling a free quantum particle by coupling an internal (discrete) state of the particle to a detector (or probe). We consider a sequence of time-dependent, spatially localized interactions of the particle with the probe that are purely coherent (nondissipative), without mean energy-momentum exchange. We show that a sequence of such force-free interactions can freeze or deflect the particle.

We present new investigations on a five-level laser cooling scheme which can be used for subrecoil cooling of the group of even-even isotopes. System dynamics and the temporal evolution of the atomic momentum distribution are examined numerically in the case of 200Hg. We prove important features, e.g. constant efficiency at long interaction times as well as the influence of relaxation of coherences on the cooling process.

We revisit the theory of tunnel-coupled atomic quasicondensates in double-well elongated traps at finite temperatures. Using the functional-integral approach, we calculate the relative-phase correlation function beyond the harmonic limit of small fluctuations of the relative phase and its conjugate relative-density variable. We show that the thermal fluctuations of the relative phase between the two quasicondensates decrease the frequency of Josephson oscillations and even wash out these oscillations for small values of the tunnel coupling., revtex4, 4 figures (.eps)

We experimentally study the relaxation dynamics of a coherently split one-dimensional Bose gas using matterwave interference. Measuring the full probability distributions of interference contrast reveals the prethermalization of the system to a non-thermal steady state. To describe the evolution of noise and correlations we develop a semiclassical effective description that allows us to model the dynamics as a stochastic Ornstein-Uhlenbeck process., Submitted to EPJ Special Topics for the special issue on "Novel Quantum Phases and Mesoscopic Physics in Quantum Gases", Lyon BEC 2012

Expansion of a degenerate Bose gas released from a pancakelike trap is numerically simulated under the assumption of separation of the motion in the plane of the loose initial trapping and the motion in the direction of the initial tight trapping. The initial conditions for the phase fluctuations are generated using the extension to the two-dimensional case of the description of the phase noise by the Ornstein-Uhlenbeck stochastic process. The numerical simulations, taking into account both the finite size of the two-dimensional system and the atomic interactions, which cannot be neglected on the early stage of expansion, did not reproduce the scaling law for the peaks in the density fluctuation spectra experimentally observed by Choi, Seo, Kwon, and Shin [Phys. Rev. Lett. 109, 125301 (2012)]. The latter experimental results may thus require an explanation beyond our current assumptions.

Einstein, Podolsky & Rosen (EPR) pointed out that correlations induced between quantum objects will persist after these objects have ceased to interact. Consequently, their joint continuous variables (CV), e.g., the difference of their positions and the sum of their momenta, may be specified, regardless of their distance, with arbitrary precision. EPR correlations give rise to two fundamental notions: {\em nonlocal ``steering''} of the quantum state of one object by measuring the other, and inseparability ({\em entanglement}) of their quantum states. EPR entanglement is a resource of quantum information (QI) and CV teleportation of light and matter waves. It has lately been demonstrated for {\em collective} CV of distant thermal-gas clouds, correlated by interaction with a common field. Here we demonstrate that collective CV of two species of trapped ultracold bosonic gases can be EPR-correlated (entangled) via {\em inherent} interactions between the species. This paves the way to further QI applications of such systems, which are atomic analogs of coupled superconducting Josephson Junctions (JJ). A precursor of this study has been the observation of quantum correlations (squeezing) in a single bosonic JJ.

We consider decay of a quasiparticle in a nearly-one-dimensional quasicondensate of trapped atoms, where virtual excitations of transverse modes break down one-dimensionality and integrability, giving rise to effective three-body elastic collisions. We calculate the matrix element for the process that involves one incoming quasiparticle and three outgoing quasiparticles. Scattering that involves low-frequency modes with high thermal population results in a diffusive dynamics of a bunch of quasiparticles created in the system., Revtex4, 4 Figures

We present numerical results demonstrating the possibility of thermalization of single-particle observables in a one-dimensional integrable system (a quasicondensate of ultra-cold, weakly-interacting bosonic atoms being studied as a definite example). These results may seem counterintuitive because the physical system is integrable in both the quantum and classical (mean-field) descriptions. However, we find a class of initial conditions that admits the relaxation of distributions of single-particle observables to the equilibrium state very close to the Bose-Einstein thermal distribution of Bogoliubov quasiparticles. Our numerical results allow us to explain experimentally observed thermalization in one-dimensional ultracold atomic gases on a short (~1 ms) time scale., Comment: revtex4, 4 figures; final version

A theoretical analysis of one-dimensional cooling of atoms is presented. The method of cooling is based on velocity-selective coherent population trapping. Both internal and translational degrees of freedom of the atoms are treated quantum mechanically. The analytic expression for atomic density matrix is obtained in the limit of large interaction time and small kinetic momentum of atom. It is demonstrated that: (i) there is a limit on the lowest temperature that can be achieved by such a method and it is determined by the small but finite rate of decay of the coherence between two low-lying states in the three-level Lambda -configuration; (ii) the fraction of atoms involved in the cooling process decreases to zero as the atom-field interaction time increases, because of the presence of such a relaxation which always takes place in real experimental systems.

We prepare a chemically and thermally one-dimensional (1d) quantum degenerate Bose gas in a single microtrap. We introduce a new interferometric method to distinguish the quasicondensate fraction of the gas from the thermal cloud at finite temperature. We reach temperatures down to $kT\approx 0.5\hbar\omega_\perp$ (transverse oscillator eigenfrequency $\omega_\perp$) when collisional thermalization slows down as expected in 1d. At the lowest temperatures the transverse momentum distribution exhibits a residual dependence on the line density $n_{1d}$, characteristic for 1d systems. For very low densities the approach to the transverse single particle ground state is linear in $n_{1d}$., Comment: to appear in Phys. Rev. Lett

We study the fluctuation properties of a one-dimensional many-body quantum system composed of interacting bosons, and investigate the regimes where quantum noise or, respectively, thermal excitations are dominant. For the latter we develop a semiclassical description of the fluctuation properties based on the Ornstein-Uhlenbeck stochastic process. As an illustration, we analyze the phase correlation functions and the full statistical distributions of the interference between two one-dimensional systems, either independent or tunnel-coupled and compare with the Luttinger-liquid theory., 4 pages (revtex4), 4 color figures. Text substantially rewritten, two figures added

Interferometry with ultracold atoms promises the possibility of ultraprecise and ultrasensitive measurements in many fields of physics, and is the basis of our most precise atomic clocks. Key to a high sensitivity is the possibility to achieve long measurement times and precise readout. Ultra cold atoms can be precisely manipulated at the quantum level, held for very long times in traps, and would therefore be an ideal setting for interferometry. In this paper we discuss how the non-linearities from atom-atom interactions on one hand allow to efficiently produce squeezed states for enhanced readout, but on the other hand result in phase diffusion which limits the phase accumulation time. We find that low dimensional geometries are favorable, with two-dimensional (2D) settings giving the smallest contribution of phase diffusion caused by atom-atom interactions. Even for time sequences generated by optimal control the achievable minimal detectable interaction energy $\Delta E^{\rm min}$ is on the order of 0.001 times the chemical potential of the BEC in the trap. From there we have to conclude that for more precise measurements with atom interferometers more sophisticated strategies, or turning off the interaction induced dephasing during the phase accumulation stage, will be necessary., Comment: 28 pages, 13 figures, extended and corrected

We numerically model the evolution of a pair of coherently split quasicondensates. A truly one-dimensional case is assumed, so that the loss of the (initially high) coherence between the two quasicondensates is due to dephasing only, but not due to the violation of integrability and subsequent thermalization (which are excluded from the present model). We confirm the subexponential time evolution of the coherence between two quasicondensates $\propto \exp [-(t/t_0)^{2/3}]$, experimentally observed by S. Hofferberth {\em et. al.}, Nature {\bf 449}, 324 (2007). The characteristic time $t_0$ is found to scale as the square of the ratio of the linear density of a quasicondensate to its temperature, and we analyze the full distribution function of the interference contrast and the decay of the phase correlation., Comment: revtex4, 9 pages, 8 figures