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arXiv:1201.3993 · Physical Review A

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

Christine Khripkov, Amichay Vardi, Doron Cohen

Published May 24, 2012• 5 citations
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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.

DOI
10.1103/physreva.85.053632

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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.
The dynamical evolution of squeezing correlations in an ultracold Bose-Einstein condensate distributed across two modes is investigated theoretically in the framework of the Bose-Hubbard model. It is shown that the eigenstates of the Hamiltonian do not exploit the full region allowed by Heisenberg's uncertainty relation for number and phase fluctuations. The development of nonclassical correlations and relative number squeezing is studied in the transition from the Josephson to the Fock regime. Comparing the full quantum evolution with classical statistical simulations allows us to identify quantum aspects of the squeezing formation. In the quantum regime, the measurement of squeezing allows us to distinguish even and odd total particle numbers.
We study the effect of decoherence on dynamical phase diffusion in the two-site Bose-Hubbard model. Starting with an odd parity excited coherent state, the initial loss of single-particle coherence varies from small bound oscillations in the Rabi regime, through hyperbolic depletion in the Josephson regime, to a Gaussian decay in the Fock regime. The inclusion of local-site noise, measuring the relative number difference between the modes, is shown to enhance phase diffusion. In comparison, site-indiscriminate noise measuring the population imbalance between the two quasimomentum modes slows down the loss of single-particle coherence. Decoherence thus either enhances or suppresses phase diffusion, depending on the details of system-bath coupling and the overlap of decoherence pointer states with collisional-entanglement pointer states. The deceleration of phase diffusion due to the coupling with the environment may be viewed as a many-body quantum Zeno effect. The extended effective decay times in the presence of projective measurement are further enhanced with increasing number of particles NNN by a bosonic factor of N\sqrt{N}N​ in the Fock regime and N/log NN/\text{log}\text{ }NN/log N in the Josephson regime.
When the rotating frequency of a noninteracting Bose-Einstein condensate (BEC) confined in a weak anisotropic harmonic potential is suddenly quenched to its trapping frequency, the condensate evolves from its ground state to a single-mode squeezed state with exponentially growing quantum fluctuation anisotropy. Such a squeezed state is called the geometrically squeezed state. However, for interacting BECs with two-body collisions, a similar quench only results in quantum fluctuations oscillating periodically without squeezing. In this work, we identify superfluid stability as the key factor behind this nonsqueezing phenomenon, with the periodic oscillations arising from collective excitations of a stable collective excitation mode. By strategically breaking the stability criteria, we propose a dynamical approach for generating squeezing that can exponentially suppress quantum fluctuations in a relatively short time, surpassing the efficiency of existing experimental preparation schemes.
Abstract We study the effect of dephasing on the spin-mixing dynamics of a spinor Bose–Einstein condensate. We focus on a short-time dynamics and derive an analytical dynamics equations for the system by using mean-field approximation. We show the spin-mixing is suppressed via a quantum Zeno effect (QZE) in which the phase-noise intensity is much stronger than the inverse correlation time of the stimulated process. We also investigate the spin-nematic squeezing in the process of spin-mixing dynamics and show the squeezing is restrained by the QZE.
We analyze a scheme that uses quantum nondemolition measurements to induce squeezing of a two-mode Bose-Einstein condensate in a double-well trap. In a previous paper [E. O. Ilo-Okeke, S. Sunami, C. J. Foot, and T. Byrnes, Phys. Rev. A 104, 053324 (2021)], we introduced a model to solve exactly the wave function for all atom-light interaction times. Here, we perform approximations for the short interaction time regime, which is relevant for producing squeezing. Our approach uses a Holstein-Primakoff approximation for the atoms while we treat the light variables exactly. It allows us to show that the measurement induces correlations within the condensate, which manifest in the state of the condensate as a superposition of even-parity states. In the long interaction time regime, our methods allow us to identify the mechanism for loss of squeezing correlation. We derive simple expressions for the variances of atomic spin variables conditioned on the measurement outcome. We find that the results agree with the exact solution in the short interaction time regime. Additionally, we show that the expressions are the sum of the variances of the atoms and the measurement. Beyond the short interaction time regime, our scheme agrees qualitatively with the exact solution for the spin variable that couples to light.