Squeezing in driven bimodal Bose-Einstein condensates: Erratic driving versus noise

Abstract

We study the interplay of squeezing and phase randomization near the hyperbolic instability of a two-site Bose-Hubbard model in the Josephson interaction regime. We obtain results for the quantum Zeno suppression of squeezing far beyond the previously found short time behavior. More importantly, we contrast the expected outcome with the case where randomization is induced by erratic driving with the same fluctuations as the quantum noise source, finding significant differences. These are related to the distribution of the squeezing factor, which has log-normal characteristics: hence its average is significantly different from its median due to the occurrence of rare events. I. INTRODUCTIONThe effect of stochastic driving on unitary evolution has been a central theme of modern quantum mechanics. It is well established that quantum decay can be suppressed by frequent interventions, or measurements, or by the introduction of noise, via the Quantum Zeno Effect (QZE) [1][2][3][4][5][6][7][8][9][10][11][12]. The modelling of the "interventions" as arising from a deterministic or from a noisy source are often used interchangeably [5][6][7][8][9]. This partially reflects the paradigm that the Langevin picture and the Master equation picture of the dynamics are equivalent.Recent work considered the QZE suppression of interaction-induced squeezing in bimodal Bose-Einstein condensates [13,14]. Since matter-wave squeezing is the key to the realization of atom interferometers below the standard quantum limit [15][16][17][18][19][20], it is highly desirable to gain better understanding of its interplay with noise. Noise was shown to arrest the squeezing and build-up of many-body correlations in the large, multi-particle system, prepared with all particles occupying the odd superposition of the two-modes. In the Josephson regime [21] this preparation constitutes a hyperbolic saddle point, leading to a rapid squeezing [22,23]. It was shown that the degree of squeezing and the associated phase diffusion [24][25][26][27][28][29] could be controlled by a noisy modulation of the coupling between the modes, up to a full arrest via a Bose-stimulated QZE [13,14].In this work we attain two principle goals. (i) We extend the analytic understanding of the QZE suppression of squeezing to time-scales which are orders of magnitude longer than these of Ref. [13,14], obtaining good agreement with numerical simulations. (ii) We challenge the fundamental paradigm of replacing quantum noise by deterministic erratic driving. Erratic driving can have nontrivial statistics, hence its typical results do not have to agree with the average behavior. This is demonstrated in our system by an important caveat resulting from the interplay of the nonlinear squeezing dynamics and the diffusive randomization by driving. While the early evolution under the influence of either noisy or erratic driving corresponds to the QZE of Ref. [13,14], significant differences arise at later times. These differences are explained by a statistical analysis: As the squeezing...

Suppression and enhancement of decoherence in an atomic Josephson junction

“…This term can be viewed as a fluctuating energy bias driving phase fluctuations. Here ( ) f t 3 is an erratic driving amplitude that we take as a Markovian random process with zero average and short correlation time [41],…”

Suppression of collision-induced dephasing by periodic, erratic, or noisy driving

“…3 shows the dynamics of the single particle coherence under the influence of erratic driving. In contrast to the drive-free dynamics (5), the orientation of the wavepacket relative to the principal squeezing axes is not constant: the erratic driving randomizes this orientation on time scale t D = 1/(2D), resulting in angular diffusion [23]. The squeezing rate is no longer constant, thus Eq.…”

“…Due to the growth of variance along the expanding axis of the squeezed Gaussian state, the one-particle coherence S decreases. Using a simple phase space picture, a good approximation for the loss of coherence is given by [23],…”

Stability and stabilization of unstable condensates

“…In the lower panel the evolution of a ϕ = π preparation is simulated in the presence of noise (thick black curve) and compared with noiseless evolution (orange curve). For more details see [14]. strated in the upper panel of Fig.3 using the Husimi representation.…”

“…The stability of such stationary state is due to the interaction. This presentation is based on [10][11][12][13][14][15][16] and further references therein [17].…”