Controlling Quantum Transport via Dissipation Engineering

Abstract

Inspired by the microscopic control over dissipative processes in quantum optics and cold atoms, we develop an open-system framework to study dissipative control of transport in strongly interacting fermionic systems, relevant for both solid state and cold atom experiments. We show how subgap currents exhibiting Multiple Andreev Reflections -the stimulated transport of electrons in the presence of Cooper-pairs -can be controlled via engineering of superconducting leads or superfluid atomic gases. Our approach incorporates dissipation within the channel, which is naturally occurring and can be engineered in cold gas experiments. This opens opportunities for engineering many phenomena with transport in strongly interacting systems. As examples, we consider particle loss and dephasing, and note different behaviour for currents with different microscopic origin. We also show how to induce nonreciprocal electron and Cooper-pair currents.Introduction. Understanding and controlling the outof-equilibrium dynamics of strongly interacting manybody systems constitutes one of the key forefronts in quantum physics across a variety of subfields in experiment and theory. In this context, opportunities to achieve their control via dissipation mechanisms have arisen [1,2], as is applied for few-body systems in quantum optics [3,4]. This is especially true in cold-atom platforms, where large separations between frequency scales allows well-controlled theoretical models and implementations of dissipative processes, as realized for laser cooling and trapping [5]. The longer timescales of cold atom experiments also allow dynamics to be tracked and potentially controlled time-dependently [6,7]. Outof-equilibrium transport dynamics remain a ubiquitous paradigm in the solid state [8], and recent developments in cold atom systems have also made it possible to engineer quantised transport of atoms between reservoirs, as well as quantum point contacts and waveguides [9][10][11][12]. Here we explore the emerging new opportunity of using dissipation engineering to achieve control of quantum transport properties, that are relevant for both coldatom and solid-state platforms.

Numerical evaluation of two-time correlation functions in open quantum systems with matrix product state methods: a comparison

“…Using the mapping to interacting fermions or hard core bosons, the jump operator corresponds to a local particle loss process. Similar 'lossy' defects have been studied in a variety of models previously and interesting transport effects and meta-stable states have been identified [45][46][47][48][49][50][51][52][53][54][55].…”

Reservoir engineering of Cooper-pair-assisted transport with cold atoms

“…The coupling strength g S = á ñW ℓ ℓ of each field is determined by the macroscopic ground state occupation S á ñ of the BEC and the Rabi frequency Ω ℓ , which can be tuned independently through different field amplitudes. It turns out that the Hamiltonian H BEC (t) well-represents the so-called proximity effects induced by s-wave superconductors of chemical potentials δ ℓ /2 and Cooper-pair tunnelling amplitudes g ℓ , when their superconducting gap is larger than the junction frequency scales [20,30]. For this reason, we consider in the following only two driving fields whose detunings are adjusted to the chemical potential of the fermionic reservoirs, i.e.,…”

“…This justifies our 'system+bath' decomposition and motivates the use of an open system approach. As in [30], we derive a Floquet-Redfield master equation, i.e. a Redfield master equation for the periodic time-dependent system [22][23][24][25]-which corresponds to the driven junction in our case.…”

“…a Redfield master equation for the periodic time-dependent system [22][23][24][25]-which corresponds to the driven junction in our case. In contrast with [30] where the reservoirs were in a gapped phase, we consider them in a normal, non-interacting phase. This allows us to show that Cooper-pair-assisted transport can be achieved between the drain and source reservoirs even if these latter do not contain any pairs.…”

“…Such a method, in addition to treat the interaction in the junction exactly, makes it possible to capture the complex interplay between driving and dissipation mechanisms, and has been applied in the context of photonassisted transport or Landau-Zener tunnelling [29]. In [30], we adapted the Floquet master equation formalism to Cooper-pair driving, which appears in quantum dot systems coupled to superconductors, and demonstrated control of Cooper-pair-assisted transport of electrons. Here, we use this framework in a cold atom context, where the driving comes from the molecular BEC and the dissipation processes correspond to coupling of atoms into and out off large (thermal) reservoirs.…”