Abstract
Describing current in open quantum systems can be problematic due to the subtle interplay of quantum coherence and environmental noise. Probing the noise-induced current can be detrimental to the tunneling-induced current and vice versa. We derive a general theory for the probability current in quantum systems arbitrarily interacting with their environment that overcomes this difficulty. We show that the current can be experimentally measured by performing a sequence of weak and standard quantum measurements. We exemplify our theory by analyzing a simple Smoluchowski–Feynman-type ratchet consisting of two particles, operating deep in the quantum regime. Fully incorporating both thermal and quantum effects, the current generated in the model can be used to detect the onset of ‘genuine quantumness’ in the form of quantum contextuality. The model can also be used to generate steady-state entanglement in the presence of arbitrarily hot environment.
Highlights
Current is a central notion in transport theory and non-equilibrium thermodynamics
Despite the considerable attention quantum transport and quantum walks in dissipative systems have received [2, 3, 4, 5, 6, 7, 8, 9, 10], there exists no general definition of quantum current in open quantum systems, which would take into account both tunneling and environment-induced hopping
Our formula describes the current even when the position operator does not commute with the system-environment interaction, which, until now, was an uncharted territory
Summary
Current is a central notion in transport theory and non-equilibrium thermodynamics. Defining quantum current in closed systems is straightforward [1]. In order to study current generation in quantum devices, one first has to deal with the fundamental problem of defining the current in open quantum systems. We solve this problem in the most general form, by deriving a surprisingly simple formula for probability current, universally applicable to systems undergoing arbitrary dynamics (be it Markovian or non-Markovian). We illustrate the power of our theory on a minimalist model of a quantum rotor, capable of autonomously generating current in the steady-state regime. Using standard techniques from the theory of open quantum systems, we fully characterize the non-equilibrium steady states of the rotor, allowing us to make a rigorous connection between the symmetries of the rotor’s Hamiltonian and the main transport properties of the system: particle current and heat flux. In the presence of sufficiently strong tunneling, powered by temperature difference, the machine can “charge” the initially “empty” (i.e., incapable of producing work) rotor with extractable work
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