We show that the nonequilibrium entropy production for a driven quantum system is larger than the Bures length, the geometric distance between its actual state and the corresponding equilibrium state. This universal lower bound generalizes the Clausius inequality to arbitrary nonequilibrium processes beyond linear response. We further derive a fundamental upper bound for the quantum entropy production rate and discuss its connection to the Bremermann-Bekenstein bound.

We treat small trapped unequal-mass two-component Fermi gases at unitarity within a nonperturbative microscopic framework and investigate the system properties as functions of the mass ratio $\kappa$, and the numbers $N_1$ and $N_2$ of heavy and light fermions. While equal-mass Fermi gases with infinitely large interspecies $s$-wave scattering length $a_s$ are universal, we find that unequal-mass Fermi gases are, for sufficiently large $\kappa$ and in the regime where Efimov physics is absent, not universal. In particular, the $(N_1,N_2)=(2,1)$ and (3, 1) systems exhibit three-body and four-body resonances at $\kappa =12.314(2)$ and 10.4(2), respectively, as well as surprisingly large finite-range effects. These findings have profound implications for ongoing experimental efforts and quantum simulation proposals that utilize unequal-mass atomic Fermi gases.

We have studied the relaxation of a spin-polarized gas in a magnetic field, in the presence of short-range spin-dependent interactions. As a main result we have established a link between the specific properties of the interaction and the dependence of the spin-relaxation rate on the magnitude of the holding magnetic field. This allows us to formulate a new, extremely sensitive method to study (pseudo) magnetic properties at the submillimeter scale, which are difficult to access by other means. The method has been used as a probe for nucleon-nucleon axionlike $P$, $T$ violating interactions which yields a two-order-of-magnitude improved constraint on the coupling strength ($g_s{g}_p$) as a function of the force range ($\lambda$): $g_s{g}_p{\lambda }^2<3\times {10}^{-27}{\mathrm{m}}^2$.

Fluctuation relations establish rigorous identities for the nonequilibrium averages of observables. Starting from a general transport master equation with time-dependent rates, we employ the stochastic path integral approach to study statistical fluctuations around such averages. We show how under nonequilibrium conditions, rare realizations of transport observables are crucial and imply massive fluctuations that may completely mask such identities. Quantitative estimates for these fluctuations are provided. We illustrate our results on the paradigmatic example of a mesoscopic $RC$ circuit.

We present a method to control the shape and character of the interaction potential between cold atomic gases by weakly dressing the atomic ground state with a Rydberg level. For increasing particle densities, a crossover takes place from a two-particle interaction into a collective many-body interaction, where the dipole-dipole or van der Waals blockade phenomenon between the Rydberg levels plays a dominant role. We study the influence of these collective interaction potentials on a Bose-Einstein condensate and present the optimal parameters for its experimental detection.

We report the numerical realization of robust two-component structures in 2D and 3D Bose-Einstein condensates with nontrivial topological charge in one component. We identify a stable symbiotic state in which a higher-dimensional bright soliton exists even in a homogeneous setting with defocusing interactions, due to the effective potential created by a stable vortex in the other component. The resulting vortex–bright-solitons, generalizations of the recently experimentally observed dark-bright solitons, are found to be very robust both in the homogeneous medium and in the presence of external confinement.

We theoretically propose a scheme for a spin quantum bit based on a double quantum dot contacted to ferromagnetic elements. Interface exchange effects enable an all electric manipulation of the spin and a switchable strong coupling to a superconducting coplanar waveguide cavity. Our setup does not rely on any specific band structure and can in principle be realized with many different types of nanoconductors. This allows us to envision on-chip single spin manipulation and readout using cavity QED techniques.

Heat conduction in three-dimensional anharmonic lattices was numerically studied by the Green-Kubo theory. For a given lattice width $W$, a dimensional crossover is generally observed to occur at a $W$-dependent threshold of the lattice length. Lattices shorter than $W$ will display a 3D behavior while lattices longer than $W$ will display a 1D behavior. In the 3D regime, the heat current autocorrelation function was found to show a power-law decay as a function of the time lag $\tau$ as ${\tau }^{\beta }$ with $\beta =-1.2$. This indicates normal heat conduction. However, the decay exponent deviates significantly from the conventional theoretical value of $\beta =-1.5$. A flat power spectrum $S(\omega )$ of the global heat current in the low-frequency limit was also observed in the 3D regime. This provides not only an alternative verification of normal heat conduction but also a clear physical insight into its origin.

An effective spin-orbit coupling can be generated in a cold atom system by engineering atom-light interactions. In this Letter we study spin-$1/2$ and spin-1 Bose-Einstein condensates with Rashba spin-orbit coupling, and find that the condensate wave function will develop nontrivial structures. From numerical simulation we have identified two different phases. In one phase the ground state is a single plane wave, and often we find the system splits into domains and an array of vortices plays the role of a domain wall. In this phase, time-reversal symmetry is broken. In the other phase the condensate wave function is a standing wave, and it forms a spin stripe. The transition between them is driven by interactions between bosons. We also provide an analytical understanding of these results and determine the transition point between the two phases.

We experimentally and theoretically demonstrate the purity (polarization) control of qubits entangled with multiple spins, using induced dephasing in nuclear magnetic resonance setups to simulate repeated quantum measurements. We show that one may steer the qubit ensemble towards a quasiequilibrium state of a certain purity by choosing suitable time intervals between dephasing operations. These results demonstrate that repeated dephasing at intervals associated with the anti-Zeno regime leads to ensemble purification, whereas those associated with the Zeno regime lead to ensemble mixing.

We propose a novel realization of Anderson localization in nonequilibrium states of ultracold atoms in an optical lattice. A Rabi pulse transfers part of the population to a different internal state with infinite effective mass. These frozen atoms create a quantum superposition of different disorder potentials, localizing the mobile atoms. For weakly interacting mobile atoms, Anderson localization is obtained. The localization length increases with increasing disorder and decreasing interaction strength, contrary to the expectation for equilibrium localization.

We propose a hybrid (continuous-discrete variable) quantum repeater protocol for long-distance entanglement distribution. Starting from states created by single-photon detection, we show how entangled coherent state superpositions can be generated by means of homodyne detection. We show that near-deterministic entanglement swapping with such states is possible using only linear optics and homodyne detectors, and we evaluate the performance of our protocol combining these elements.

We study a cold atom-molecule mixture in two-dimensional optical lattices. We show that, by fine-tuning the atomic and molecular interactions, the Wess-Zumino supersymmetry (SUSY) model in $2+1$ dimensions emerges in the low-energy limit and can be simulated in such mixtures. At zero temperature, SUSY is not spontaneously broken, which implies identical relativistic dispersions of the atom and its superpartner, a bosonic diatom molecule. This defining signature of SUSY can be probed by single-particle spectroscopies. Thermal breaking of SUSY at a finite temperature is accompanied by a thermal Goldstone fermion, i.e., phonino excitation. This and other signatures of broken SUSY can also be probed experimentally.

We present an exact calculation of the mean first-passage time to a small target on the surface of a 2D or 3D spherical domain, for a molecule performing surface-mediated diffusion. This minimal model of interfacial reactions, which explicitly takes into account the combination of surface and bulk diffusion, shows the importance of correlations induced by the coupling of the switching dynamics to the geometry of the confinement, ignored so far. Our results show that, in the context of interfacial systems in confinement, the reaction time can be minimized as a function of the desorption rate from the surface, which puts forward a general mechanism of enhancement and regulation of chemical and biological reactivity.

In this Letter we show that the time reversal asymmetry of a stationary time series provides information about the entropy production of the physical mechanism generating the series, even if one ignores any detail of that mechanism. We develop estimators for the entropy production which can detect nonequilibrium processes even when there are no measurable flows in the time series.

We study the efficiency at maximum power, ${\eta }^{*}$, of engines performing finite-time Carnot cycles between a hot and a cold reservoir at temperatures $T_h$ and $T_c$, respectively. For engines reaching Carnot efficiency ${\eta }_C=1-T_c/T_h$ in the reversible limit (long cycle time, zero dissipation), we find in the limit of low dissipation that ${\eta }^{*}$ is bounded from above by ${\eta }_C/(2-{\eta }_C)$ and from below by ${\eta }_C/2$. These bounds are reached when the ratio of the dissipation during the cold and hot isothermal phases tend, respectively, to zero or infinity. For symmetric dissipation (ratio one) the Curzon-Ahlborn efficiency ${\eta }_{\mathrm{CA}}=1-\sqrt{T_c/T_h}$ is recovered.

In the Hilbert space formulation of classical mechanics, pioneered by Koopman and von Neumann, there are potentially more observables than in the standard approach to classical mechanics. In this Letter, we show that actually many of those extra observables are not invariant under a set of universal local symmetries which appear once the Koopman and von Neumann formulation is extended to include the evolution of differential forms. Because of their noninvariance, those extra observables have to be removed. This removal makes the superposition of states in the Koopman and von Neumann formulation, and as a consequence also in classical mechanics, impossible.

We investigate the dynamics of a one-dimensional Bose gas after a quench from the Tonks-Girardeau regime to the regime of strong attractive interactions applying analytical techniques and numerical simulations. After the quench the system is found to be predominantly in an excited gaslike state, the so-called super-Tonks gas, however with a small coherent admixture of two-particle bound states. Despite its small amplitude, the latter leads to a pronounced oscillation of the local density correlation with a frequency corresponding to the binding energy of the pair. Contributions from bound states with larger particle numbers are found to be negligible.

A generalization of the $ABC$ model, a one-dimensional model of a driven system of three particle species with local dynamics, is introduced, in which the model evolves under either (i) density-conserving or (ii) nonconserving dynamics. For equal average densities of the three species, both dynamical models are demonstrated to exhibit detailed balance with respect to a Hamiltonian with long-range interactions. The model is found to exhibit two distinct phase diagrams, corresponding to the canonical (density-conserving) and grand canonical (density nonconserving) ensembles, as expected in long-range interacting systems. The implications of this result to nonequilibrium steady states, such as those of the $ABC$ model with unequal average densities, are briefly discussed.

We establish methods for quantum state tomography based on compressed sensing. These methods are specialized for quantum states that are fairly pure, and they offer a significant performance improvement on large quantum systems. In particular, they are able to reconstruct an unknown density matrix of dimension $d$ and rank $r$ using $O(rd{log}^{2}d)$ measurement settings, compared to standard methods that require $d^2$ settings. Our methods have several features that make them amenable to experimental implementation: they require only simple Pauli measurements, use fast convex optimization, are stable against noise, and can be applied to states that are only approximately low rank. The acquired data can be used to certify that the state is indeed close to pure, so no a priori assumptions are needed.