arXiv:cond-mat/0608732

Quantum Spin Dynamics of Spin-1 Bose Gas

Roberto B. Diener, Tin-Lun Ho

Published Aug 31, 2006• 7 citations

Abstract

We show that the quantum evolution of a spin-1 Bose gas with nearly all bosons initially in the $F_z = 0$ state has a "quantum carpet" {\em spin-time} structure with self-similar properties. The system continuously evolves into "multi-peaked" Schrödinger cat like states, returning occasionally to coherent structures, which leads to large number fluctuations (as seen in recent experiments). The self similar behavior allows one to reveal the quantum evolution as a set of peaks in the number probability distribution of a spin component at times {\em much shorter} than the quantum revival time. We also show that these features survive small number fluctuations among spin components up to a few percent.

DOI: 10.48550/arxiv.cond-mat/0608732

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arXiv:cond-mat/0608732

Quantum Spin Dynamics of Spin-1 Bose Gas

Roberto B. Diener, Tin-Lun Ho

Published Aug 31, 2006• 7 citations

arXiv HTML PDF

Abstract

We show that the quantum evolution of a spin-1 Bose gas with nearly all bosons initially in the

F_z = 0

state has a "quantum carpet" {\em spin-time} structure with self-similar properties. The system continuously evolves into "multi-peaked" Schrödinger cat like states, returning occasionally to coherent structures, which leads to large number fluctuations (as seen in recent experiments). The self similar behavior allows one to reveal the quantum evolution as a set of peaks in the number probability distribution of a spin component at times {\em much shorter} than the quantum revival time. We also show that these features survive small number fluctuations among spin components up to a few percent.

DOI: 10.48550/arxiv.cond-mat/0608732

Related papers

Fractional revivals, multiple-Schrödinger-cat states, and quantum carpets in the interaction of a qubit with N qubits

Shane Dooley, Timothy P. Spiller

We study the dynamics of a system comprised of a single qubit interacting equally with $N$ qubits (a ``spin star'' system). Although this model can be solved exactly, the exact solution does not give much intuition for the dynamics of the model. Here, we find an approximation that gives some insight into the dynamics for a particular class of initial spin-coherent states of the $N$ qubits. We find an effective Hamiltonian for the system that is a finite Kerr (one-axis twisting) Hamiltonian for the $N+1$ qubits. The initial spin-coherent state evolves to spin-squeezed states on short time scales, and to ``multiple-Schr\"odinger-cat'' states (superpositions of many spin-coherent states) on longer time scales, a manifestation of the phenomenon of fractional revivals of the initial state. The evolution of the system is visualized with phase-space plots ( $Q$ functions) that, when plotted against time, reveal a ``quantum carpet'' pattern. Of particular interest is the fact that our approximation captures the qualitative features of the model even for small values of $N$ . This suggests the possibility of observing the phenomenon of fractional revival in this model for systems of few qubits.We study the dynamics of a system comprised of a single qubit interacting equally with $N$ qubits (a ``spin star'' system). Although this model can be solved exactly, the exact solution does not give much intuition for the dynamics of the model. Here, we find an approximation that gives some insight into the dynamics for a particular class of initial spin-coherent states of the $N$ qubits. We find an effective Hamiltonian for the system that is a finite Kerr (one-axis twisting) Hamiltonian for the $N+1$ qubits. The initial spin-coherent state evolves to spin-squeezed states on short time scales, and to ``multiple-Schr\"odinger-cat'' states (superpositions of many spin-coherent states) on longer time scales, a manifestation of the phenomenon of fractional revivals of the initial state. The evolution of the system is visualized with phase-space plots ($Q$ functions) that, when plotted against time, reveal a ``quantum carpet'' pattern. Of particular interest is the fact that our approximation captures the qualitative features of the model even for small values of $N$. This suggests the possibility of observing the phenomenon of fractional revival in this model for systems of few qubits.

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Coherent seeding of the dynamics of a spinor Bose-Einstein condensate: From quantum to classical behavior

Bertrand Evrard, An Qu, Jean Dalibard +1 more

arXiv:2101.06716Physical Review AMar 3, 202113 citations

We show that the quantum evolution of a spin-1 Bose gas with nearly all bosons initially in the

F_z = 0

We study the dynamics of a system comprised of a single qubit interacting equally with

N

qubits (a ``spin star'' system). Although this model can be solved exactly, the exact solution does not give much intuition for the dynamics of the model. Here, we find an approximation that gives some insight into the dynamics for a particular class of initial spin-coherent states of the

N

qubits. We find an effective Hamiltonian for the system that is a finite Kerr (one-axis twisting) Hamiltonian for the

N+1

qubits. The initial spin-coherent state evolves to spin-squeezed states on short time scales, and to ``multiple-Schr\"odinger-cat'' states (superpositions of many spin-coherent states) on longer time scales, a manifestation of the phenomenon of fractional revivals of the initial state. The evolution of the system is visualized with phase-space plots (

Q

functions) that, when plotted against time, reveal a ``quantum carpet'' pattern. Of particular interest is the fact that our approximation captures the qualitative features of the model even for small values of

N

. This suggests the possibility of observing the phenomenon of fractional revival in this model for systems of few qubits.

We study the spin-mixing dynamics of an

f=1

spinor condensate. We show that the dynamics is sensitive to the relative phase and particle number distribution among the individual components of the condensate, and find that complex structures can develop in the density profiles during the time evolution. We investigate the different time scales of the spin-mixing process and their dependence on the total particle number.