Sindre Brattegard, Thomás Fogarty, Thomas Busch
et al.
We theoretically investigate the correlated decoherence dynamics of two mobile impurities trapped within a gas of ultracold fermionic atoms. We use a mean-field approximation to self-consistently describe the effect of impurity-gas collisions on impurity motion, while decoherence of the impurities' internal state is computed exactly within a functional determinant approach. At equilibrium, we find that the impurities undergo bath-induced localisation as the impurity-gas interaction strength is increased. We then study the non-equilibrium dynamics induced by a sudden change of the impurities' internal state, which can be experimentally probed by Ramsey interferometry. Our theoretical approach allows us to investigate the effect of impurity motion on decoherence dynamics, finding strong deviations from the universal behaviour associated with Anderson's orthogonality catastrophe when the mass imbalance between impurity and gas atoms is small. Finally, we show that mobile impurities can be used as thermometers of their environment and that bath-mediated correlations can be beneficial for thermometric performance at low temperatures, even in the presence of non-trivial impurity motion. Our results showcase the interesting open quantum dynamics of mobile impurities dephasing in a common environment, and could help provide more precise temperature estimates of ultracold fermionic mixtures.
We present a comprehensive review on the state-of-the-art of the approximate analytic approaches describing the finite-temperature thermodynamic quantities of the Lieb-Liniger model of the one-dimensional (1D) Bose gas with contact repulsive interactions. This paradigmatic model of quantum many-body-theory plays an important role in many areas of physics -- thanks to its integrability and possible experimental realization using, e.g., ensembles of ultracold bosonic atoms confined to quasi-1D geometries. The thermodynamics of the uniform Lieb-Liniger gas can be obtained numerically using the exact thermal Bethe ansatz (TBA) method, first derived in 1969 by Yang and Yang. However, the TBA numerical calculations do not allow for the in-depth understanding of the underlying physical mechanisms that govern the thermodynamic behavior of the Lieb-Liniger gas at finite temperature. Our work is then motivated by the insights that emerge naturally from the transparency of closed-form analytic results, which are derived here in six different regimes of the gas and which exhibit an excellent agreement with the TBA numerics. Our findings can be further adopted for characterising the equilibrium properties of inhomogeneous (e.g., harmonically trapped) 1D Bose gases within the local density approximation and for the development of improved hydrodynamic theories, allowing for the calculation of breathing mode frequencies which depend on the underlying thermodynamic equation of state. Our analytic approaches can be applied to other systems including impurities in a quantum bath, liquid helium-4, and ultracold Bose gas mixtures.
Yunpeng Ji, Grant L. Schumacher, Gabriel G. T. Assumpção
et al.
We report the creation and the study of the stability of a repulsive quasi-homogeneous spin-$1/2$ Fermi gas with contact interactions. For the range of scattering lengths $a$ explored, the dominant mechanism of decay is a universal three-body recombination towards a Feshbach bound state. We observe that the recombination coefficient $K_3\propto ε_\text{kin} a^6$, where the first factor, the average kinetic energy per particle $ε_\text{kin}$, arises from a three-body threshold law, and the second one from the universality of recombination. Both scaling laws are consequences of Pauli blocking effects in three-body collisions involving two identical fermions. As a result of the interplay between Fermi statistics and the momentum dependence of the recombination process, the system exhibits non-trivial temperature dynamics during recombination, alternatively heating or cooling depending on its initial quantum degeneracy. The measurement of $K_3$ provides an upper bound for the interaction strength achievable in equilibrium for a uniform repulsive Fermi gas.
The quantum kicked rotor is well-known for displaying dynamical (Anderson) localization. It has recently been shown that a periodically kicked Tonks gas will always localize and converge to a finite energy steady-state. This steady-state has been described as being effectively thermal with an effective temperature that depends on the parameters of the kick. Here we study a generalization to a quasi-periodic driving with three frequencies which, without interactions, has a metal-insulator Anderson transition. We show that a quasi-periodically kicked Tonks gas goes through a dynamical many-body delocalization transition when the kick strength is increased. The localized phase is still described by a low effective temperature, while the delocalized phase corresponds to an infinite-temperature phase, with the temperature increasing linearly in time. At the critical point, the momentum distribution of the Tonks gas displays different scaling at small and large momenta (contrary to the non-interacting case), signaling a breakdown of the one-parameter scaling theory of localization.
Lena H. Dogra, Gevorg Martirosyan, Timon A. Hilker
et al.
Boyle's 1662 observation that the volume of a gas is, at constant temperature, inversely proportional to pressure, offered a prototypical example of how an equation of state (EoS) can succinctly capture key properties of a many-particle system. Such relations are now cornerstones of equilibrium thermodynamics. Extending thermodynamic concepts to far-from-equilibrium systems is of great interest in various contexts including glasses, active matter, and turbulence, but is in general an open problem. Here, using a homogeneous ultracold atomic Bose gas, we experimentally construct an EoS for a turbulent cascade of matter waves. Under continuous forcing at a large length scale and dissipation at a small one, the gas exhibits a non-thermal, but stationary state, which is characterised by a power-law momentum distribution sustained by a scale-invariant momentum-space energy flux. We establish the amplitude of the momentum distribution and the underlying energy flux as equilibrium-like state variables, related by an EoS that does not depend on the details of the energy injection or dissipation, or the history of the system. Moreover, we show that the equations of state for a wide range of interaction strengths and gas densities can be empirically scaled onto each other. This results in a universal dimensionless EoS that sets benchmarks for the theory and should also be relevant for other turbulent systems.
Thibault Scoquart, Thomas Wellens, Dominique Delande
et al.
We theoretically study the out-of-equilibrium dynamics in momentum space of a weakly interacting disordered Bose gas launched with a finite velocity. In the absence of interactions, coherent multiple scattering gives rise to a background of diffusive particles, on top of which a coherent backscattering interference emerges. We revisit this scenario in the presence of interactions, using a diagrammatic quantum transport theory. We find that the dynamics is governed by coupled kinetic equations describing the thermalization of the diffusive and coherent components of the gas. This phenomenon leads to a destruction of coherent backscattering, well described by an exponential relaxation whose rate is controlled by the particle collision time. These predictions are confirmed by numerical simulations.
Benjamin Reichert, Aleksandra Petkovic, Zoran Ristivojevic
We study the fluctuation-induced interaction between two impurities in a weakly-interacting one-dimensional Bose gas using the field theoretical approach. At separations between impurities shorter and of the order of the healing length of the system, the induced interaction has a classical origin and behaves exponentially. At separations longer than the healing length, the interaction is of a quantum origin and scales as the third power of the inverse distance. Finite temperature destroys the quasi-long-range order of the Bose gas and, accordingly, the induced interaction becomes exponentially suppressed beyond the thermal length. We obtain analytical expressions for the induced interaction at zero and finite temperature that are valid at arbitrary distances. We discuss experimental realizations as well as possible formation of bound states of two impurities, known as bipolarons.
Lena H. Dogra, Jake A. P. Glidden, Timon A. Hilker
et al.
Three-body recombination in quantum gases is traditionally associated with heating, but it was recently found that it can also cool the gas. We show that in a partially condensed three-dimensional homogeneous Bose gas three-body loss could even purify the sample, that is, reduce the entropy per particle and increase the condensed fraction $η$. We predict that the evolution of $η$ under continuous three-body loss can, depending on small changes in the initial conditions, exhibit two qualitatively different behaviours - if it is initially above a certain critical value, $η$ increases further, whereas clouds with lower initial $η$ evolve towards a thermal gas. These dynamical effects should be observable under realistic experimental conditions.
We investigate the ground-state energy of a one-dimensional Fermi gas with two bosonic impurities. We consider spinless fermions with no fermion-fermion interactions. The fermion-impurity and impurity-impurity interactions are modelled with Dirac delta functions. First, we study the case where impurity and fermions have equal masses, and the impurity-impurity two-body interaction is identical to the fermion-impurity interaction, such that the system is solvable with the Bethe ansatz. For attractive interactions, we find that the energy of the impurity-impurity subsystem is below the energy of the bound state that exists without the Fermi gas. We interpret this as a manifestation of attractive boson-boson interactions induced by the fermionic medium, and refer to the impurity-impurity subsystem as an in-medium bound state. For repulsive interactions, we find no in-medium bound states. Second, we construct an effective model to describe these interactions, and compare its predictions to the exact solution. We use this effective model to study non-integrable systems with unequal masses and/or potentials. We discuss parameter regimes for which impurity-impurity attraction induced by the Fermi gas can lead to the formation of in-medium bound states made of bosons that repel each other in the absence of the Fermi gas.
We demonstrate that the partial entropy of a two-dimensional electron gas (2DEG) exhibits quantized peaks at resonances between the chemical potential and electron levels of size quantization. In the limit of no scattering, the peaks depend only on the subband quantization number and are independent on material parameters, shape of the confining potential, electron effective mass and temperature. The quantization of partial entropy is a signature of a topological phase transition in a 2DEG. In the presence of stationary disorder, the magnitude of peaks decreases. Its deviation from the quantized values is a direct measure of the disorder induced smearing of the electronic density of states.
We investigate the possibility that the broken spatial inversion symmetry by a trap potential induces a spin-triplet Cooper-pair amplitude in an $s$-wave superfluid Fermi gas. Being based on symmetry considerations, we clarify that this phenomenon may occur, when a spin rotation symmetry of the system is also broken. We also numerically confirm that a triplet pair amplitude is really induced under this condition, using a simple model. Our results imply that this phenomenon is already present in a trapped $s$-wave superfluid Fermi gas with spin imbalance. As an interesting application of this phenomenon, we point out that one may produce a $p$-wave superfluid Fermi gas, by suddenly changing the $s$-wave pairing interaction to a $p$-wave one by using the Feshbach resonance technique. Since a Cooper pair is usually classified into the spin-singlet (and even-parity) state and the spin-triplet (and odd-parity) state, our results would be useful in considering how to mix them with each other in a superfluid Fermi gas. Such admixture has recently attracted much attention in the field of non-centrosymmetric superconductivity, so that our results would also contribute to the further development of this research field, on the viewpoint of cold Fermi gas physics.
A. K. Fedorov, I. L. Kurbakov, Y. E. Shchadilova
et al.
We predict the effect of the roton instability for a two-dimensional weakly interacting gas of tilted dipoles in a single homogeneous quantum layer. Being typical for strongly correlated systems, the roton phenomena appear to occur in a weakly interacting gas. It is important that in contrast to a system of normal to wide layer dipoles, breaking of the rotational symmetry for a system of tilted dipoles leads to the convergence of the condensate depletion even up to the threshold of the roton instability, with mean-field approach being valid. Predicted effects can be observed in a wide class of dipolar systems. We suggest observing predicted phenomena for systems of ultracold atoms and polar molecules in optical lattices, and estimate optimal experimental parameters.