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Journal of Experimental and Theoretical Physics Letters

Atomic condensate in an optical trap formed by a cavity mode

L. V. Il’ichev

Published Jul 1, 2017• 4 citations
Publisher

Abstract

It has been shown that an optical trap for an atomic condensate formed by a mode of a ring cavity possesses specific properties. These properties are not featured by a trap formed by free beams and arise owing to quantum correlations (entanglement) between the localized atoms and the optical mode. In particular, there is an effect similar to an optomechanical phenomenon known as an “optical spring” (S. Martellucci et al., Bose–Einstein Condensates and Atom Lasers (Kluwer, Dordrecht, 2002)) and manifested by the emergence of an effective correction to the interaction between the localized atoms. The magnitude and sign of this correction can be controlled by varying the frequency of the source forming the trap.

DOI
10.1134/s0021364017130094

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It has been shown that an optical trap for an atomic condensate formed by a mode of a ring cavity possesses specific properties. These properties are not featured by a trap formed by free beams and arise owing to quantum correlations (entanglement) between the localized atoms and the optical mode. In particular, there is an effect similar to an optomechanical phenomenon known as an “optical spring” (S. Martellucci et al., Bose–Einstein Condensates and Atom Lasers (Kluwer, Dordrecht, 2002)) and manifested by the emergence of an effective correction to the interaction between the localized atoms. The magnitude and sign of this correction can be controlled by varying the frequency of the source forming the trap.
We develop a fully quantized model of a Bose-Einstein condensate driven by a far off-resonant pump laser and interacting with a single mode of an optical ring cavity. This geometry leads to the generation of two condensate side modes that grow exponentially and are strongly entangled with the cavity mode. By changing the initial state of the optical field one can vary the quantum-statistical properties of the atomic side modes between thermal and coherent limits, as well as vary the degree of quantum entanglement.
The dispersive interaction of a Bose-Einstein condensate with a single mode of a high-finesse optical cavity realizes the radiation pressure coupling Hamiltonian. In this system the role of the mechanical oscillator is played by a single condensate excitation mode that is selected by the cavity mode function. We study the effect of atomic s-wave collisions and show that it merely renormalizes parameters of the usual optomechanical interaction. Moreover, we show that even in the case of strong harmonic confinement – which invalidates the use of Bloch states – a single excitation mode of the Bose-Einstein condensate couples significantly to the light field, that is the simplified picture of a single "mechanical" oscillator mode remains valid.
Optical trapping as a viable means of exploring the physics of ultracold dilute atomic gases has revealed a new spectrum of physical phenomena. In particular, macroscopic and sudden occupation of the ground state below a critical temperature—-a phenomenon known as Bose-Einstein condensation—-has become an even richer system for the study of quantum mechanics, ultracold collisions, and many-body physics in general. Optical trapping liberates the spin degree of the BEC, making the order parameter vectorial (‘spinor BEC’), as opposed to the scalar order of traditional magnetically trapped condensates. The work described within is divided into two main efforts. The first encompasses the all-optical creation of a Bose-Einstein condensate in rubidium vapor. An all-optical path to spinor BEC (as opposed to transfer to an optical trap from a magnetic-trap condensate) was desired both for the simplicity of the experimental setup and also for the potential gains in speed of creation; evaporative cooling, the only known path to dilute-gas condensation, works only as efficiently as the rate of elastic collisions in the gas, a rate that starts out much higher in optical traps. The first all-optical BEC was formed elsewhere in 2001; the years following saw many groups worldwide seeking to create their own version. Our own all-optical spinor BEC, made with a single-beam dipole trap formed by a focused CO₂ laser, is described here, with particular attention paid to trap loading, measurement of trap parameters, and the use of a novel 780 nm high-power laser system. The second part describes initial experiments performed with the nascent condensate. The spinor properties of the condensate are documented, and a measurement is made of the density-dependent rate of spin mixing in the condensate. In addition, we demonstrate a novel dual-beam atom laser formed by outcoupling oppositely polarized components of the condensate, whose populations have been coherently evolved through spin dynamics. We drive coherent spin-mixing evolution through adiabatic compression of the initially weak trap. Such dual beams, nominally number-correlated through the angular momentum-conserving collision m=0 + m=0 ⇌ m=+1 + m=-1 have been proposed as tools to explore entanglement and squeezing in Bose-Einstein condensates.
We propose a method to generate entangled light with a Bose–Einstein condensate trapped in a cavity, a system realized in recent experiments. The atoms of the condensate are trapped in a periodic potential generated by a cavity mode. The condensate is continuously pumped by a laser and spontaneously emits a pair of photons of different frequencies in two distinct cavity modes. In this way, the condensate mediates entanglement between two cavity modes, which leak out and can be separated and exhibit continuous variable entanglement. The scheme exploits the experimentally demonstrated strong, steady and collective coupling of condensate atoms to a cavity field.
We propose a method to generate entangled light with a Bose-Einstein condensate trapped in a cavity, a system realized in recent experiments. The atoms of the condensate are trapped in a periodic potential generated by a cavity mode. The condensate is continuously pumped by a laser and spontaneously emits a pair of photons of different frequencies in two distinct cavity modes. In this way, the condensate mediates entanglement between two cavity modes, which leak out and can be separated and exhibit continuous variable entanglement. The scheme exploits the experimentally demonstrated strong, steady and collective coupling of condensate atoms to a cavity field.