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arXiv:1607.05605 · Physical Review Letters

Nonexponential Decoherence and Subdiffusion in Atom-Optics Kicked Rotor

Sumit Sarkar, Sanku Paul, Chetan Vishwakarma, Sunil Kumar, Gunjan Verma, M. Sainath, Umakant D. Rapol, M. S. Santhanam

Published Apr 26, 2017• 35 citations
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Abstract

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.

DOI
10.1103/physrevlett.118.174101

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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.
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.
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 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.
We develop a theory describing the dynamics of quantum kicked rotators (modeling cold atoms in a pulsed optical field) which are subjected to combined amplitude and timing noise generated by a renewal process (acting as an engineered reservoir). For waiting-time distributions of variable exponent (L\'evy noise), we demonstrate the existence of a regime of nonexponential loss of phase coherence. In this regime, the momentum dynamics is subdiffusive, which also manifests itself in a non-Gaussian limiting distribution and a fractional power-law decay of the inverse participation ratio. The purity initially decays with a stretched exponential which is followed by two regimes of power-law decay with different exponents. The averaged logarithm of the fidelity probes the sprinkling distribution of the renewal process. These analytical results are confirmed by numerical computations on quantum kicked rotators subjected to noise events generated by a Yule-Simon distribution.
Atom-optics kicked rotor represents an experimentally realizable version of the paradigmatic quantum kicked rotor system. After a short initial diffusive phase the cloud settles down to a stationary state due to the onset of dynamical localization. In this work we realise an enhancement of localization by modification of the kick sequence. We experimentally implement the modification to this system in which the sign of the kick sequence is flipped by allowing for a free evolution of the wavepackets for half the Talbot time after every MMM kicks. Depending on the value of MMM, this modified system displays a combination of enhanced diffusion followed by asymptotic localization. This is explained as resulting from two competing processes -- localization induced by standard kicked rotor type kicks, and diffusion induced by half Talbot time evolution. The evolving states display a localized but non-exponential wave function profiles. This provides another route to quantum control in kicked rotor class of systems. The numerical simulations agree well with the experimental results.
Atom-optics kicked rotor represents an experimentally reliable version of the paradigmatic quantum kicked rotor system. In this system, a periodic sequence of kicks are imparted to the cold atomic cloud. After a short initial diffusive phase the cloud settles down to a stationary state due to the onset of dynamical localization. In this paper, to explore the interplay between localized and diffusive phases, we experimentally implement a modification to this system in which the sign of the kick sequence is flipped after every M kicks. This is achieved in our experiment by allowing free evolution for half the Talbot time after every M kicks. Depending on the value of M, this modified system displays a combination of enhanced diffusion followed by asymptotic localization. This is explained as resulting from two competing processes-localization induced by standard kicked rotor type kicks, and diffusion induced by the half Talbot time evolution. The experimental and numerical simulations agree with one another. The evolving states display localized but nonexponential wave function profiles. This provides another route to quantum control in the kicked rotor class of systems.