玻色—爱因斯坦凝聚体的腔光力学
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摘要
在最近几年中腔光力学正经历着飞速的发展,成为了大量理论与实验研究的焦点。其中十分诱人的一项进展是使用原子玻色-爱因斯坦凝聚体取代被光压驱动的腔镜展示出各种腔光力学效应。而本文则设计了一个将凝聚体与腔镜结合在一起的混合腔光力学系统,试图通过这个系统把光学、腔量子电动力学、超冷原子物理、凝聚态物理、纳米技术、量子信息等学科交融在了一起来推动腔光力学的发展。本文的内容可根据原子与腔相互作用的不同区域而分成两个部分。
当腔与原子的相互作用处于弱色散耦合区域时,腔内的驻波光场会使原子凝聚体感受到一个周期性的偶极势——光晶格,但凝聚体作为色散介质对腔场的影响却可以忽略不计。腔内光场的强度由于腔镜位置与光压之间的非线性耦合而具有双稳的性质,而这种双稳性质也同样反映在了光晶格的深度以及取决于这个深度的凝聚体多体基态上。同一个输入光强可以使腔内的凝聚体处于超流或者绝缘这两种迥然不同的状态,而对输入光进行特殊的时序控制,则可能实现凝聚体的双稳量子相变。尤其是在双稳切换点附近光场强度发生跳变时,原子凝聚体的动力学是本文的研究重点之一。
当腔与原子的相互作用处于强色散耦合区域时,腔内的凝聚体被驻波光场激发出的动量边模能够等效为一个光压驱动的腔镜。而驻波场除了驱动凝聚体和腔镜外还像一个非线性的弹簧一样把两者连接起来形成一对非线性耦合振子。在适当的参量下,整个系统,无论是腔内光强,腔镜位置,还是凝聚体的激发都是双稳的。我们发现在这个双稳区域附近,如果忽略系统的耗散,则其经典动力学能够展现奇异的哈密顿混沌行为。此外我们还在频率空间中分析了腔镜与凝聚体之间的量子关联,给出了两者之间实现纠缠的条件。
Cavity optomechanics is currently the focus of extensive theoretical and ex-perimental investigations and has witnessed spectacular advances in the last few years. An impressive progress was the demonstration of optomechanics effects in situations where the radiation-pressure-driven mechanical oscillator is replaced by a Bose-Einstein condensate. In this thesis I present a hybrid optomechanical system consisting of a BEC trapped inside a single-mode optical cavity with a moving end mirror. This system opens the way to the exploration of a completely new regime of interaction among light, ultracold atoms, and quantum-mechanical nanostructures. I particularly focus on two regime of the interaction between the condensate and the cavity.
In collective-dispersive-weak couping regime, the cavity-induced dipole forces provide an optical lattice potential which is collectively sensed by the condensate, but the retro-action of the condensate as a dispersive medium on the cavity field is negligible. Due to the radiation pressure, the lattice depth dynamically depends on the position of the moving mirror, causing a bistable quantum many-body ground state, super-fluid state or Mott-insulator state, of the condensate. We predict a bistable quantum phase transition in this state when the optomechan-ical cavity controlled by a time-dependent input field, and focus on the atomic dynamics following discontinuous jumps of the lattice depth.
In collective-dispersive-strong couping regime, the intra-cavity light field has a dual role:it excites a momentum side mode of the condensate which is formally identical with a mechanical oscillator, and acts as a nonlinear spring that couples this oscillator to the moving mirror. We present the dynamics in a regime where the intra-cavity optical field, the mirror, and the side-mode excitation all display bistable behavior. In this regime we find that the classical dynamics of the system exhibits Hamiltonian chaos for appropriate initial condition. We also analyze the quantum correlation between the mirror and the side-mode excitation, predict the possibility of creating a robust entanglement between them in frequency domain.
当腔与原子的相互作用处于弱色散耦合区域时,腔内的驻波光场会使原子凝聚体感受到一个周期性的偶极势——光晶格,但凝聚体作为色散介质对腔场的影响却可以忽略不计。腔内光场的强度由于腔镜位置与光压之间的非线性耦合而具有双稳的性质,而这种双稳性质也同样反映在了光晶格的深度以及取决于这个深度的凝聚体多体基态上。同一个输入光强可以使腔内的凝聚体处于超流或者绝缘这两种迥然不同的状态,而对输入光进行特殊的时序控制,则可能实现凝聚体的双稳量子相变。尤其是在双稳切换点附近光场强度发生跳变时,原子凝聚体的动力学是本文的研究重点之一。
当腔与原子的相互作用处于强色散耦合区域时,腔内的凝聚体被驻波光场激发出的动量边模能够等效为一个光压驱动的腔镜。而驻波场除了驱动凝聚体和腔镜外还像一个非线性的弹簧一样把两者连接起来形成一对非线性耦合振子。在适当的参量下,整个系统,无论是腔内光强,腔镜位置,还是凝聚体的激发都是双稳的。我们发现在这个双稳区域附近,如果忽略系统的耗散,则其经典动力学能够展现奇异的哈密顿混沌行为。此外我们还在频率空间中分析了腔镜与凝聚体之间的量子关联,给出了两者之间实现纠缠的条件。
Cavity optomechanics is currently the focus of extensive theoretical and ex-perimental investigations and has witnessed spectacular advances in the last few years. An impressive progress was the demonstration of optomechanics effects in situations where the radiation-pressure-driven mechanical oscillator is replaced by a Bose-Einstein condensate. In this thesis I present a hybrid optomechanical system consisting of a BEC trapped inside a single-mode optical cavity with a moving end mirror. This system opens the way to the exploration of a completely new regime of interaction among light, ultracold atoms, and quantum-mechanical nanostructures. I particularly focus on two regime of the interaction between the condensate and the cavity.
In collective-dispersive-weak couping regime, the cavity-induced dipole forces provide an optical lattice potential which is collectively sensed by the condensate, but the retro-action of the condensate as a dispersive medium on the cavity field is negligible. Due to the radiation pressure, the lattice depth dynamically depends on the position of the moving mirror, causing a bistable quantum many-body ground state, super-fluid state or Mott-insulator state, of the condensate. We predict a bistable quantum phase transition in this state when the optomechan-ical cavity controlled by a time-dependent input field, and focus on the atomic dynamics following discontinuous jumps of the lattice depth.
In collective-dispersive-strong couping regime, the intra-cavity light field has a dual role:it excites a momentum side mode of the condensate which is formally identical with a mechanical oscillator, and acts as a nonlinear spring that couples this oscillator to the moving mirror. We present the dynamics in a regime where the intra-cavity optical field, the mirror, and the side-mode excitation all display bistable behavior. In this regime we find that the classical dynamics of the system exhibits Hamiltonian chaos for appropriate initial condition. We also analyze the quantum correlation between the mirror and the side-mode excitation, predict the possibility of creating a robust entanglement between them in frequency domain.
引文
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