Bosonic transport through a chain of quantum dots

Abstract

The particle transport through a chain of quantum dots coupled to two bosonic reservoirs is studied. For the case of reservoirs of non-interacting bosonic particles, we derive an exact set of stochastic differential equations, whose memory kernels and driving noise are characterised entirely by the properties of the reservoirs. Going to the Markovian limit an analytically solvable case is presented. The effect of interparticle interactions on the transient behaviour of the system, when both reservoirs are instantaneously coupled to an empty chain of quantum dots, is approximated by a semiclassical method, known as the Truncated Wigner approximation. The steady-state particle flow through the chain and the mean particle occupations are explained via the spectral properties of the interacting system.

Non‐equilibrium dynamics in dissipative Bose‐Hubbard chains

“…This means that for large voltages the transport of the particles through the lattice is blocked. The same qualitative behavior was observed in [38] by approximating the interaction contribution to the selfenergy by the tabpole diagram, in the non-equilibrium Green's function framework. The blockade is a consequence of the interactions: as we saw in Fig.…”

“…As in refs. [38,39] we are interested explicitly in the transport of neutral atoms, not in heat conductance across the sample as studied, e.g. in refs.…”

Two-Time Correlation Functions in Dissipative and Interacting Bose–Hubbard Chains

“…An alternative approach would be then to fully include the leads into the treatment and use a diagrammatic expansion of the Green functions computed for the full lead-system-lead system, such as done for bosons in steady state in Refs. [42,43]. Needless to say, such an approach as just mentioned is very hard for many-body quantum systems whose main central part, without the leads, is itself non-integrable, such as our many-body Bose-Hubbard model for more than two wells [44,45].…”

Towards an Atomtronic Diode

“…Both findings together verify the predicted dependence: τ −1 eff ∝ J 2 =Γ dec . Conclusions.-The observation of NDC in the transport of ultracold quantum gases bears great potential for future implementations of interaction controlled atomic circuits [14,15,[36][37][38][39]. It can also serve as an alternative mechanism for the observation of bistability and related nonequilibrium phenomena.…”