Pure and truly nonclassical noise-induced transitions at the microscopic scale

Abstract

It is universally accepted that noise may bring order to complex nonequilibrium systems. Most strikingly, entirely new states not seen in the noiseless system can be induced purely by including multiplicative noise-an effect known as pure noise-induced transitions. It was first observed in superfluids in the 1980s. Recent results in complex nonequilibrium systems have also shown how new collective states emerge from such pure noise-induced transitions, such as the foraging behavior of insect colonies, and schooling in fish. Here we report such effects of noise in a quantum-mechanical system. We find that multiplicative quantum noise can induce a classically forbidden transition. We use a minimal model of a nonlinearly damped oscillator in a fluctuating environment that is analytically tractable, and whose microscopic physics can be understood. When environmental noise is included, the system is seen to transition to a limit-cycle state. The noise-induced quantum limit cycle exhibits genuine nonclassical traits such as Wigner negativity and number-parity sensitive circulation in phase space. Such quantum limit cycles are also conservative. These properties are in stark contrast to those of a widely used limit cycle in the literature, which is dissipative and loses all Wigner negativity. Our results establish the existence of a pure noise-induced transition that is nonclassical and unique to open quantum systems. They illustrate a fundamental difference between quantum and classical noise.

Quantum synchronization effects induced by strong nonlinearities

“…To define amplitude death in quantum oscillators, we generalize the notion of P-bifurcations from classical stochastic systems to the steady-state Wigner function of a reduced state (see Ref. [18] and other references therein). In this case, amplitude death is said to occur if the singleoscillator Wigner functions peak at the origin in quantum phase space.…”

“…Another widely recognized effect is noise-induced transitions [17]. Recent work has extended this effect to quantum mechanics by using a quantum stochastic differential equation and its correspondence to nonlinear dissipation [18] (see also Ref. [19]).…”

Quantum synchronization effects induced by strong nonlinearities

“…To define amplitude death in quantum oscillators we generalize the notion of P-bifurcations from classical stochastic systems to the steady-state Wigner function of a reduced state (see Ref. [57] and other references therein). In this case, amplitude death is said to occur if the single-oscillator Wigner functions peak at the origin in quantum phase space.…”

Quantum synchronization: insights and applications to quantum information processing

“…To define amplitude death in quantum oscillators we generalize the notion of P-bifurcations from classical stochastic systems to the steady-state Wigner function of a reduced state (see Ref. [CMNK22] and other references therein). In this case, amplitude death is said to occur if the single-oscillator Wigner functions peak at the origin in quantum phase space.…”