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arXiv:1407.2804 · Physical Review A

Nonequilibrium relaxation transport of ultracold atoms

Fernando Gallego-Marcos, Gloria Platero, Christian Nietner, Gernot Schaller, Tobias Brandes

Published Sep 15, 2014• 27 citations
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Abstract

We analyze the equilibration process between two either fermionic or bosonic reservoirs containing ultracold atoms with a fixed total number of particles that are weakly connected via a few-level quantum system. We allow for both the temperatures and particle densities of the reservoirs to evolve in time. Subsequently, linearizing the resulting equations enables us to characterize the equilibration process and its time scales in terms of equilibrium reservoir properties and linear-response transport coefficients. Additionally, we investigate the use of such a device as particle transistor or particle capacitor and analyze its efficiency.

DOI
10.1103/physreva.90.033614

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We present a formalism to study many-particle quantum transport across a lattice locally connected to two finite, nonstationary (bosonic or fermionic) reservoirs, both of which are in a thermal state. We show that, for conserved total particle number, a system of nonlinear quantum-classical master equations describes the concurrent many-particle time evolution on the lattice and in the reservoirs. The finiteness of the reservoirs makes a macroscopic current emerge, which decreases exponentially in time and asymptotically drives the many-particle configuration into an equilibrium state where the particle flow ceases. We analytically derive the timescale of this equilibration process, and, furthermore, investigate the imprint of many-particle interferences on the transport process.
When driven by a potential bias between two finite reservoirs, the particle current across a quantum system evolves from an initial loading through a coherent, followed by a metastable phase, and ultimately fades away upon equilibration. We formulate a theory which fully accounts for the associated, distinct time scales, and identifies the parameter dependence of the decay rate which ultimately controls the convergence towards equilibrium. Our formalism guarantees total particle number conservation and fundamental consistency between macroscopic and internal currents flowing in the system. We furthermore establish a clear imprint of the fermionic or bosonic particle character on the resulting conductance.
A gas of interacting ultracold fermions can be tuned into a strongly interacting regime using a Feshbach resonance. Here, we theoretically study quasiparticle transport in a system of two reservoirs of interacting ultracold fermions on the BCS side of the BCS-BEC crossover coupled weakly via a tunnel junction. Using the generalized BCS theory, we calculate the time evolution of the system that is assumed to be initially prepared in a nonequilibrium state characterized by a particle number imbalance or a temperature imbalance. A number of characteristic features like sharp peaks in quasiparticle currents or transitions between the normal and superconducting states are found. We discuss signatures of the Seebeck and the Peltier effects and the resulting temperature difference of the two reservoirs as a function of the interaction parameter ${({k}_{F}a)}^{\ensuremath{-}1}$. The Peltier effect may lead to an additional cooling mechanism for ultracold fermionic atoms.
We propose experimental protocols to reveal thermoelectric and thermal effects in the transport properties of ultracold fermionic atoms, using the two-terminal setup recently realized at ETH. We show in particular that, for two reservoirs having equal particle numbers but different temperatures initially, the observation of a transient particle number imbalance during equilibration is a direct evidence of thermoelectric (off-diagonal) transport coefficients. This is a time-dependent analogue of the Seebeck effect, and a corresponding analogue of the Peltier effect can be proposed. We reveal that in addition to the thermoelectric coupling of the constriction a thermoelectric coupling also arises due to the finite dilatation coefficient of the reservoirs. We present a theoretical analysis of the protocols, and assess their feasibility by estimating the corresponding temperature and particle number imbalances in realistic current experimental conditions.
We study energy and particle transport for one-dimensional strongly interacting bosons through a ballistic single channel connecting two atomic reservoirs. We show the emergence of particle- and energy-current separation, leading to the violation of the Wiedemann-Franz law. As a consequence, we predict different time scales for the equilibration of temperature and particle imbalances between the reservoirs. Going beyond the linear spectrum approximation, we show the emergence of thermoelectric effects, which could be controlled by either tuning interactions or the temperature. Our results describe, in a unified picture, fermions in condensed-matter devices and bosons in ultracold atom setups. We conclude by discussing the effects of a controllable disorder.