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arXiv:1506.02910 · Journal of Modern Optics

Cavity-mediated collective laser-cooling of a non-interacting atomic gas inside an asymmetric trap to very low temperatures

Oleg Kim, Prasenjit Deb, Almut Beige

Published Mar 7, 2018• 7 citations
arXivHTMLPDF

Abstract

In this paper, we identify a many-particle phonon expectation value ζ with the ability to induce collective dynamics in a non-interacting atomic gas inside an optical cavity. We then propose to utilise this expectation value to enhance the laser cooling of many atoms through a cyclic two-stage process which consists of cooling and displacement stages. During cooling stages, short laser pulses are applied. These use ζ as a resource and decrease the vibrational energy of the atomic gas by a fixed amount. Subsequent displacement stages use the asymmetry of the trapping potential to replenish the many-particle phonon expectation value ζ. Alternating both stages of the cooling process is shown to transfer the atomic gas to a final temperature which vanishes in the infinitely-many particle limit.

DOI
10.1080/09500340.2018.1444800

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In this paper, we identify a many-particle phonon expectation value ζ with the ability to induce collective dynamics in a non-interacting atomic gas inside an optical cavity. We then propose to utilise this expectation value to enhance the laser cooling of many atoms through a cyclic two-stage process which consists of cooling and displacement stages. During cooling stages, short laser pulses are applied. These use ζ as a resource and decrease the vibrational energy of the atomic gas by a fixed amount. Subsequent displacement stages use the asymmetry of the trapping potential to replenish the many-particle phonon expectation value ζ. Alternating both stages of the cooling process is shown to transfer the atomic gas to a final temperature which vanishes in the infinitely-many particle limit.
In this paper, we identify a quantum coherence with the ability to induce collective dynamics in an atomic gas, when a cooling laser is applied. When present, the mean phonon number per particle changes at a rate, which is proportional to the total number of particles in the system. We then propose to use this effect to cool atoms in a cyclic two-stage process to very low temperatures. During each displacement stage, the atoms move freely inside an asymmetric trapping potential, thereby accumulating away from its centre. During each cooling stage, a cooling laser is applied, which returns the atoms to the centre of the trap, while decreasing their mean phonon number. Alternating both stages is shown to transfer the atoms to a final temperature, which vanishes in the infinitely-many particle limit.
In this thesis, we investigate dynamics of many-body atomic systems coupled to electromagnetic fields. We find that collective effects present in cavity-mediated laser cooling and high temperatures of bubble in sonoluminescence can be explained using a two-stage model which combines quantum-optical models and thermodynamical processes. We show how the collective processes are strongly dependent on mutual atomic coherences and how these coherences need to be recreated for the continous collective processes to take place. The model mechanism behind both cavity-mediated laser cooling and sonoluminescence heating is alternating periods of thermalisation with cooling or heating cycles. The thermalisation stage is characterised by relatively weak interactions between the atomic system and its environment, while allowing the system to thermalise and to create phonon and electronic coherences necessary for the next stage. The second stage, when cooling or heating occurs, marks strong interactions of the atomic system with the surrounding radiation field, which renders interactions between the particles negligible. During this stage, the atomic coherences created earlier fuel the cooling or heating process, allowing the system to reach a more beneficial stationary state. For cavity-mediated laser cooling of an atomic gas, we show that dispersing cooling pulses with periods of thermalisation in an asymmetric potential can result in very low temperatures of the atomic gas. By applying this to atomic interactions of sonoluminescence, we can describe different parts of the lifecycle of the cavitating bubble and how very high temperatures arise inside of it.
We discuss a scheme to cool, trap and manipulate an ensemble of polarizable particles moving in the field of a multimode optical cavity via the correlated dynamics of the field and the particle motion. Using a large detuning between the atoms and the field, spontaneous emission plays a negligible role in the dynamics and the cooling scheme only requires a sufficiently large optical dipole moment. Increasing the particle number slows down the cooling process but it can be accelerated using an increasing number of field modes with higher pump amplitudes. For the special case of a two mode ring cavity and assuming small deviations of the particle positions from the potential minima, the frequencies and damping rates of the vibrational excitation modes can be explicitly calculated. We find a rapid damping of the centre-of-mass motion and relatively slow damping rates for the relative particle oscillations. These predictions agree quite well with a quantum treatment of the atomic motion as used for the excitations of a non-interacting Bose gas (at T = 0) inside the cavity field. Due to the position-dependent mode coupling, the cooling process in a multimode configuration in general happens much faster than for a standing wave geometry. These analytical results are confirmed by N-particle simulations of the semiclassical equations and show even enhanced damping due to the anharmonicity of the full potential.
We study the dynamics of a multispecies mixture of laser-illuminated polarizable particles moving inside an optical resonator. Above a certain pump threshold the collective enhanced scattering of laser light into the cavity induces a phase transition from a homogeneous spatial distribution to a common crystalline order. We analytically show that adding particles of any mass and temperature always strictly lowers the minimum pump power required for self-ordering and trapping. This allows to capture and trap new species of atoms, molecules or even polarizable nanoparticles in combination with proven examples, for which a high phase-space density is readily available. Cooperative light scattering mediates effective energy exchange and thus sympathetic cooling between different species without the need for direct collisional interaction. The predicted ordering thresholds and cooling timescales are in the range of current technology for particles with a wide range of mass, polarizability and initial temperature.
We present a microscopic laser model for many atoms coupled to a single-cavity mode, including the light forces, which result from atom-field momentum exchange. Within a semiclassical description, we solve the equations for the atomic motion and the internal dynamics to obtain analytic expressions for the optical potential and the friction force seen by each atom. When optical gain is maximum at frequencies where the light field extracts kinetic energy from the atomic motion, the dynamics combines optical lasing and motional cooling. From the corresponding momentum-diffusion coefficient we predict sub-Doppler temperatures in the stationary state. This generalizes the theory of cavity-enhanced laser cooling to active cavity systems. We identify the gain-induced reduction of the effective resonator linewidth as the key origin for the faster cooling and the lower temperatures, which implies that a bad cavity with a gain medium can replace a high-QQQ cavity. In addition, this shows the importance of light forces for gas lasers in the low-temperature limit, where atoms can arrange in a periodic pattern maximizing gain and counteracting spatial hole burning. Ultimately, in the low-temperature limit, such a setup should allow us to combine optical lasing and atom lasing in a single device.
We propose a mechanism for the collective cooling of a large number N of trapped particles to very low temperatures by applying red-detuned laser fields and coupling them to the quantized field inside an optical resonator. The dynamics is described by what appears to be rate equations, but where some of the major quantities are coherences and not populations. The cooperative behaviour of the system provides cooling rates of the same order of magnitude as the cavity decay rate κ. This constitutes a significant speed-up compared to other cooling mechanisms since κ can, in principle, be as large as times the single-particle cavity or laser coupling constant.