We investigate decoherence in the quantum kicked rotator (modeling cold atoms in a pulsed optical field) subjected to noise with power-law tail waiting-time distributions of variable exponent (Lévy noise). We demonstrate the existence of a regime of nonexponential decoherence where the notion of a decoherence rate is ill defined. In this regime, dynamical localization is never fully destroyed, indicating that the dynamics of the quantum system never reaches the classical limit. We show that this leads to quantum subdiffusion of the momentum, which should be observable in an experiment.
Quantum systems upon interaction with the environment undergo decoherence or decay towards classical states. The dynamics of the quantum coherence at the borderline between quantum and classical world is not fully understood yet. The quantum coherence is generally known to exponentially decay in time so that macroscopic quantum superpositions are not sustained for a long time. In many practical applications, it is necessary to maintain quantum coherences for as long as possible. In this work, we use the experimental test-bed of cold atoms in a pulsed one-dimensional optical lattice to realise an atom-optics kicked rotator. We manipulate the waiting time between consequent kicks in this system by taking it as a random variable from a L\'{e}vy distribution. In this noisy scenario, we show that coherence can be made to decay slower than an exponential form. This manifests in the form of quantum subdiffusion that can be controlled through the L\'{e}vy exponent. The experimental results are in good agreement with the analytical expressions and numerical simulations for the mean energy growth of atom-optics kicked rotor.
Quantum systems lose coherence upon interaction with the environment and tend towards classical states. Quantum coherence is known to exponentially decay in time so that macroscopic quantum superpositions are generally unsustainable. In this work, slower than exponential decay of coherences is experimentally realized in an atom-optics kicked rotor system subjected to nonstationary Lévy noise in the applied kick sequence. The slower coherence decay manifests in the form of quantum subdiffusion that can be controlled through the Lévy exponent. The experimental results are in good agreement with the analytical estimates and numerical simulations for the mean energy growth and momentum profiles of an atom-optics kicked rotor.
The dynamics of chaotic Hamiltonian systems such as the kicked rotor continues to guide our understanding of transport and localization processes. The localized states of the quantum kicked rotor decay due to decoherence effects if subjected to noise. The associated quantum diffusion increases monotonically as a function of a parameter characterizing the noise distribution. In this Rapid Communication, for the atom-optics Lévy kicked rotor, the quantum diffusion displays nonmonotonic behavior as a function of a parameter characterizing the Lévy distribution. The optimal diffusion rates are experimentally obtained using an ultracold cloud of rubidium atoms in a pulsed optical lattice. The parameters for optimal diffusion rates are obtained analytically and show a good agreement with our experimental and numerical results. The nonmonotonicity is shown to be a quantum effect that vanishes in the classical limit.
We study the effects of non-Hermiticity on quantum coherence via a noisy quantum kicked rotor (NQKR). The random noise comes from the fluctuations in kick amplitude at each time. The non-Hermitian driving indicates the imaginary kicking potential, representing the environment-induced atom gain and loss. In the absence of gain and loss, the random noise destroys quantum coherence manifesting dynamical localization, which leads to classical diffusion. Interestingly, in the presence of non-Hermitian kicking potential, the occurrence of dynamical localization is highly sensitive to the gain and loss, manifesting the restoration of quantum coherence. Using the inverse participation ratio arguments, we numerically obtain a phase diagram of the classical diffusion and dynamical localization on the parameter plane of noise amplitude and non-Hermitian driving strength. With the help of analysis on the corresponding quasieigenstates, we achieve insight into dynamical localization, and uncover that the origin of the localization is interference between multiple quasi-eigenstates of the quantum kicked rotor. We further propose an experimental scheme to realize the NQKR in a dissipative cold atomic gas, which paves the way for future experimental investigation of an NQKR and its anomalous non-Hermitian properties.
Let
Lu be a symmetric Levy process representing an unobserved phase lift, coupling to a quantum system via charge
Q. Averaging
eiLuQ gives a completely positive dephasing semigroup. If the characteristic exponent lacks an intrinsic charge scale, the Levy-Khintchine theorem forces
η(ξ)=D∣ξ∣α (
0<α≤2), so coherences decay at
Γab=D∣qa−qb∣α. For integer charge differences, the process descends to the wrapped variable
Θu=Lumod2π; for real charges, the lift is the relevant phase. Schoenberg's theorem ensures complete positivity for any finite real spectrum when
0<α≤2, while
α>2 yields an analytic obstruction. This boundary is exact, verified numerically here.
A Gaussian integrated phase gives quadratic charge dependence, though colored Gaussian noise need not yield a Markov semigroup. Two idealized non-Gaussian mechanisms are analyzed: inverse-power Poisson shot noise (
α=d/p) and Bochner subordination of Brownian phase by an
α/2-stable clock. For a bounded reduction walk, we prove Born probabilities for every symmetric bounded proposal law. Simulations of truncated stable laws (
α=0.5,1,1.5,2) confirm this law-independence. In continuous time,
α-stable drivers fail to reduce: the exact-flow (Marcus) equation oscillates, and the naive Ito jump equation fails to preserve state. For Gaussian white noise, the Itô model collapses to Born probabilities, whereas the exact-flow (Stratonovich) model does not collapse without a threshold and yields non-Born exit probabilities. The quadratic case recovers Milburn's small-step limit, not his exact Poisson dynamics. Finally, a bi-temporal geometry is examined as a possible compact phase source, but closed timelike curves, nonunitary evolution, and an unstable mode tower prevent a consistent field-theoretic realization.