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Physical Review A

Quantum dynamics of a molecular matter-wave amplifier

Jing Cheng, YiJing Yan

Published Mar 26, 2007• 1 citation
Publisher

Abstract

We study the quantum dynamics of a model of molecular matter-wave amplifier proposed by Search and Meystre [Phys. Rev. Lett. 93, 140405 (2004)], which employs a strongly damped optical cavity to convert an atomic Bose-Einstein condensate into vibrational ground-state molecules. By using the Monte Carlo wave-function method, we calculate the quantum evolution of the atomic and molecular matter waves. We find that the system always evolves into a pure ground-state molecular matter wave even if initially there was no ground-state molecules. Statistical properties of these atomic and molecular matter waves are also investigated. The final state of the molecular field is sub-Poissonian. Two-mode correlation functions exhibit anticorrelated properties.

DOI
10.1103/physreva.75.033614

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We study the quantum dynamics of a model of molecular matter-wave amplifier proposed by Search and Meystre [Phys. Rev. Lett. 93, 140405 (2004)], which employs a strongly damped optical cavity to convert an atomic Bose-Einstein condensate into vibrational ground-state molecules. By using the Monte Carlo wave-function method, we calculate the quantum evolution of the atomic and molecular matter waves. We find that the system always evolves into a pure ground-state molecular matter wave even if initially there was no ground-state molecules. Statistical properties of these atomic and molecular matter waves are also investigated. The final state of the molecular field is sub-Poissonian. Two-mode correlation functions exhibit anticorrelated properties.
We describe a matter-wave amplifier for vibrational ground-state molecules which uses a Feshbach resonance to first form quasibound molecules starting from an atomic Bose-Einstein condensate. The quasibound molecules are then driven into their stable vibrational ground state via a two-photon Raman transition inside an optical cavity. The transition from the quasibound state to the electronically excited state is driven by a classical field. Amplification of ground state molecules is then achieved by using a strongly damped cavity mode for the transition from the electronically excited molecules to the molecular ground state.
Based on a two-mode boson model, we study nonclassical properties of the atom-molecule Bose-Einstein condensate. The effects of nonlinear collisions on the dynamics of the molecular formation is studied both in classical and quantum treatments. We find that the conversion from atoms to molecules can be suppressed strongly due to nonlinearity induced localization of the atomic population. In addition, we study statistical properties of the atom-molecule condensed system by calculating the intensity correlation functions numerically. We find that the effect of nonlinearity leads to the appearance of superchaotic molecular pulses, while maintaining the atomic field sub-Poissonian. The joint quantum statistical properties of the atoms and the molecules always show antibunching.
We study the system of coupled atomic and molecular condensates within the two-mode model and beyond mean-field theory. Large-amplitude atom-molecule coherent oscillations are shown to be damped by the rapid growth of fluctuations near the dynamically unstable molecular mode. This result contradicts earlier predictions about the recovery of atom-molecule oscillations in the two-mode limit. The frequency of the damped oscillation is also shown to scale as N/lnN\sqrt{N}/\mathrm{ln}NN​/lnN with the total number of atoms N, rather than the expected pure N\sqrt{N}N​ scaling. Using a linearized model, we obtain analytical expressions for the initial depletion of the molecular condensate in the vicinity of the instability, and show that the important effect neglected by mean-field theory is an initially nonexponential ``spontaneous'' dissociation into the atomic vacuum. Starting with a small population in the atomic mode, the initial dissociation rate is sensitive to the exact atomic amplitudes, with the fastest (superexponential) rate observed for the entangled state formed by spontaneous dissociation.
This dissertation contains a study of ultracold atoms in optical cavities. We particularly focus on two aspects of the coupled atom-cavity systems. In the first aspect, we implement the quantum nature of the light field to probe the quantum state of the atoms. This is interesting due to the nondestructive nature of the characterization of many-body atomic states. In the second aspect we study the cavity optomechanics that investigates the coupling of mechanical and optical degrees of freedom via radiation pressure. The optomechanical cavity provides an interesting nonlinear system to study the coupling between atoms and the intracavity field.In the context of cavity quantum electrodynamics we study the reflection of two counter-propagating modes of the light field in a high-Q ring cavity by ultracold atoms either in the Mott insulator state or in the superfluid state of an optical lattice. We find that the dynamics of the reflected light strongly depends on both the lattice spacing and the state of the matter-wave field. By using the Monte Carlo wave-function method to account for the cavity damping we also determine the two-time correlation function and the time-dependent physical spectrum of theretroreflected field. We find that the light field and the atoms become entangled if the latter are in a superfluid state. We also analyze quantitatively the entanglement between the atoms and the light.In cavity optomechanics the mechanical effect can either comes from a vibrating macroscopic oscillator or a collective density excitation of a Bose-Einstein condensate. First we use a Fabry-Perot-type cavity to study the opto-mechanically-induced bistable quantum phase transitions between superfluid and a Mott insulator states of an ultracold bosonic gases trapped inside the cavity. Secondly, we study the symmetricand antisymmetric collective density side modes of the BEC which results from the optomechanical effects of the light fields in a ring cavity.
Abstract We investigate the chaotic dynamics of a coupled three-level atom–molecular Bose–Einstein condensate system composed by one molecular mode and two atomic modes. With the increase of atom–molecular coupling strength, we reveal the emergence of chaotic oscillations of the relative population difference between two atomic modes, which can be proven by the broad windows with a huge number of frequencies in spectral density and the chaotic trajectories in phase space diagrams. The different effects of initial states on atomic population oscillations are revealed, where for more particles in the initial state of the molecular model, chaos appears in the larger parameter region of system dynamics. Furthermore, we find that strong intermolecular interaction strength can suppress chaos resulting from strong atom–molecule coupling. This is due to the difficult transformation between atomic and molecular modes, as well as the relatively independent dynamic evolution of atoms and molecules.
It was first realized by Purcell (1) that the spontaneous emission rate of a quantum system can be enhanced or suppressed by placing it in a resonant radiofrequency cavity. Spontaneous emission as it was first theoretically described by Einstein (2) is not a pure property of matter. It is described by matter coupled to quantized radiation field modes, which can be manipulated in an artificial structure such as a cavity. Cavity quantum electrodynamics (QED) is used to describe such effects that intimately depend on the fact that light is made of photons. Cavity QED has been extensively studied in atoms and the experimental proof was awarded with the Nobel Prize in 2012 (3). It has been applied to cooling of single atoms and for the detection of single atoms and creating and studying states with few photons and few atoms (4). In more recent developments these ideas have been extended to manipulate electronic states (5) and vibrations in molecules (6, 7). In PNAS, Flick et al. (8) introduce recent theoretical developments for the application of cavity QED to molecules and suggest possible novel applications to photochemistry. These include nonadiabatic dynamics of molecules in cavities, the modification of molecular properties, and the integration of QED with density functional theory. A quantized electromagnetic field mode can be described as a harmonic oscillator whose coordinate is the electric field displacement (Fig. 1 A ). The zero point energy translates into a nonvanishing field intensity ⟨ e 2 ⟩ in the ground state | 0 ⟩ (vacuum fluctuations). The electric vacuum field increases for a small cavity volume e c = ℏ ω c V ϵ 0 , [1] Fig. 1. ( A ) Illustration of the standing wave cavity mode and the resulting field quantization (Fock states). ( B ) Combined matter-field states (dressed states, | ± , n ⟩ … [↵][1]1To whom correspondence should be addressed. Email: smukamel{at}uci.edu. [1]: #xref-corresp-1-1