Sub-ballistic behavior in the quantum kicked rotor

Romanelli, A.; Auyuanet, A.; Siri, R.; Micenmacher, V.

doi:10.1016/j.physleta.2007.01.015

Cited by 11 publications

(24 citation statements)

References 26 publications

(26 reference statements)

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confidence: 86%

“…We show that this noise in the secondary resonances of the QKR and in the usual QW produces a change from ballistic to subballistic behavior. This change of behavior is similar to that obtained for both systems when they are subjected to an aperiodic Fibonacci excitation [10,11].Lévy distribution.-We consider two time step unitary operators U 0 and U 1 in a large sequence to generate the dynamics of the quantum system. The time interval for the alternation of U 0 and U 1 is generated by a waiting time distribution ρ(∆T ), where ∆T = iT with T a time step and i an integer.…”

supporting

confidence: 72%

“…It is calculated with κ 1 = 0.5, κ 2 = −0.5 and α = 1. The value of c remains unchanged when p/q is changed for (q − p) /q; this symmetry in c being a consequence of the trivial symmetry of the time step evolution operator U as was shown in [10]. We have verified that the exponent c has a de- pendence with the strength parameters κ 1 and κ 2 and its range is always between 0.5 and 1, thus the sub-ballistic behavior is maintained.…”

supporting

confidence: 68%

“…With the aim to generate the dynamics of the system we consider two values of the strength parameter κ 1 and κ 2 , and combine the corresponding time step operators U 0 = U (κ 1 ) and U 1 = U (κ 2 ) in a large sequence. We have proved in [10] that the ballistic behavior is maintained in the primary resonances for any type of sequences of the operators U 0 and U 1 because the operators U 0 and U 1 commute. For the same reason the antiresonance p/q = 1/2 is not changed.…”

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confidence: 93%

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Sub-ballistic behavior in quantum systems with Lévy noise

2007

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We investigate the quantum walk and the quantum kicked rotor in resonance subjected to noise with a Lévy waiting time distribution. We find that both systems have a sub-ballistic wave function spreading as shown by a power-law tail of the standard deviation.PACS numbers: PACS: 03.67. 05.40.Fb; 05.45.Mt In the last decades the study of simple quantum systems, such as the quantum kicked rotor (QKR) [1] and the quantum walk (QW) [2], have exposed unexpected behaviors that suggest new challenges both theoretical and experimental in the field of quantum information processing [3]. The behavior of the QKR has two characteristic modalities: dynamical localization (DL) and ballistic spreading of the variance in resonance. These different behaviors depend on whether the period of the kick is a rational or irrational multiple of 4π. For rational multiples the behavior of the system is resonant and the average energy grows ballistically and for irrational multiples the average energy of the system grows, for a short time, in a diffusive manner and afterwards DL appears. Quantum resonance is a constructive interference phenomena and DL is a destructive one. The DL and the ballistic behavior have already been observed experimentally [4,5]. On the other hand the concept of QW introduced in [6,7] is a counterpart of the classical random walk. Its most striking property is its ability to spread over the line linearly in time, this means that the standard deviation grows as σ(t) ∼ t, while in the classical walk it grows as σ(t) ∼ t 1/2 . We have developed [8,9] a parallelism between the behavior of the QKR and a generalized form of the QW showing that these models have similar dynamics. In [10] we have investigated the resonances of the QKR subjected to an excitation that follows an aperiodic Fibonacci prescription; there we proved that the primary resonances retain their ballistic behavior while the secondary resonances show a sub-ballistic wave function spreading (σ(t) ∼ t c with 0.5 < c < 1) like the QW with the same prescription for the coin [11]. Casati et al. [12] have studied the dynamics of the QKR kicked according to a Fibonacci sequence outside the resonant regime, they found sub-diffusive behavior for small kicking strengths and a threshold above which the usual diffusion is recovered. More recently Schomerus and Lutz [13] investigated the QKR subjected to a Lévy noise [14] and they show that this decoherence never fully destroys the DL of the QKR but leads to a sub-diffusion regime * Corresponding author. E-mail address: alejo@fing.edu.uy for a short time before DL appears.In this article we investigate the QKR in resonant regime and the usual QW when both are subjected to decoherence with a Lévy noise. In the case of the QKR the model has two strength parameters whose action alternate in a such way that the time interval between them follows a power law distribution. In the case of QW the model uses two evolution operators whose alternation follows the same power law distribution. We show that this noise in the...

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supporting

confidence: 86%

supporting

confidence: 72%

supporting

confidence: 68%

mentioning

confidence: 93%

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Sub-ballistic behavior in quantum systems with Lévy noise

2007

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“…More precisely, subballistic wave packet spreading induced by quasiperiodic Fibonacci kick sequences has been established both away and at resonance [39,40]. The effect of Lévy noise at resonance has also been the subject of a recent study [41]. An important difference to the present study is the fact that these studies do not consider the simultaneous presence of the periodic kicks in the intervals between the noise events.…”

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confidence: 74%

Controlled decoherence in a quantum Lévy kicked rotator

Schomerus

Lutz

2008

Phys. Rev. A

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We develop a theory describing the dynamics of quantum kicked rotators (modelling 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 (Lévy 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.

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