Squeezing in driven bimodal Bose-Einstein Condensates:
Erratic driving versus noise
Christine Khripkov1
M.Sc. advisor: Amichay Vardi1 Co-advisor: Doron Cohen2
Departments of Chemistry1 and Physics2, Ben-Gurion University of the Negev
The two-site Bose-Hubbard Hamiltonian has three different regimes of dynamics, depending on the ratio of the interaction term to the coupling term. Focusing on the Josephson regime, the interaction causes the initial SU(2) coherent states to squeeze: fluctuations in one direction are decreased at the expense of increased fluctuations in the perpendicular direction. The state most affected by the interaction is the antisymmetric superposition of the two sites, corresponding to the hyperbolic point (θ,φ)=(π/2,π) on the Bloch sphere. By adding different types of noise to the system it is possible to influence the squeezing and to control the fluctuations in different directions. This is an example of the quantum Zeno effect: the noise serves as "measurements" of an observable, thus arresting its evolution and protecting its initial value.
We study the interplay of squeezing and noise-induced phase randomization near the hyperbolic instability [1], and obtain analytical results for the quantum Zeno suppression of squeezing far beyond the previously found [2,3] short time behavior. The noisy driving is compared with the case where the randomization is induced by an erratic driving, with the same fluctuations as in the quantum noise source. The significant differences found between the two processes are related to the log-normal distribution of the squeezing factor, as its average is significantly different from its median due to the occurrence of rare events.
Extending the study of the noiseless long time coherence dynamics to any state on the Bloch sphere [4], we find the surprisingly simple factorization: the variance of the long time fluctuations of the Bloch vector can be described to an excellent approximation by a product of the inverse participation number, 1/M, which depends only on the initial state, and a semi-classical function, C(E), which reflects the phase space characteristics of the Bloch vector components.
1. C. Khripkov, A. Vardi and D. Cohen, Squeezing in driven bimodal Bose-Einstein Condensates: Erratic driving versus noise, submitted (2012), arXiv:1201.3993.
2. C. Khripkov and A. Vardi, Quantum Zeno control of coherent dissociation,
Phys. Rev. A 84, 021606(R) (2011), arXiv:1110.1952.
3. Y. Khodorkovsky, G. Kurizki, and A. Vardi, Phase-diffusion dynamics in weakly coupled Bose-Einstein condensates, Phys. Rev. Lett. 100, 220403 (2008); Decoherence and entanglement in a bosonic Josephson junction: Bose-enhanced quantum-Zeno control of phase-diffusion, Phys. Rev. A 80, 023609 (2009).
4. C. Khripkov, D. Cohen and A. Vardi, Temporal fluctuations in the bosonic Josephson junction as a probe for phase-space tomography, submitted (2012), arXiv:1204.324.
