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A quantum approach to cavity mediated laser cooling

Tony Blake

Published Sep 1, 2011• 0 citations
OpenAlex

Abstract

Cavity-mediated cooling has the potential to become one of the most efficient techniques to cool molecular species down to very low temperatures. This thesis studies the use of rate equations to analyse the cooling process in such systems. In particular the master equation is used to find rate equations that can determine the rate of change of phonons in the system. The general idea behind cavity cooling is the continuous conversion of phonons into cavity photons. While there is no spontaneous emission and decay rate associated with the concept of phonons, photons are created after a change in the phonon number has occurred and can then leak out through the cavity mirrors easily. Hence the conversion of phonons into photons can result in the constant removal of phonon energy from the system. In this thesis we compare cavity mediated cooling with single particle laser cooling. It is shown that cavity cooling is essentially the same as ordinary laser cooling. This is done by calculating the stationary state phonon number mss and the cooling rate y as a function of the system parameters. For example, when the trap phonon frequency υ is either much larger or much smaller than the cavity decay rate k , the minimum stationary state phonon number scales as k²/16v² (strong confinement regime) and as k/4 (weak confinement regime), respectively. Replacing k with Ѓ yields the steady states associated with ordinary laser cooling.

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Cavity-mediated cooling has the potential to become one of the most efficient techniques to cool molecular species down to very low temperatures. In this paper we analyse cavity cooling with single-laser driving for relatively large cavity decay rates κ and relatively large phonon frequencies ν. It is shown that cavity cooling and ordinary laser cooling are essentially the same within the validity range of the Lamb–Dicke approximation. This is done by deriving a closed set of rate equations and calculating the corresponding stationary state phonon number and cooling rate. For example, when ν is either much larger or much smaller than κ, the minimum stationary state phonon number scales as κ2/16ν2 (strong confinement regime) and as κ/4ν (weak confinement regime), respectively.

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Cavity-mediated cooling has the potential to become one of the most efficient techniques to cool molecular species down to very low temperatures. This thesis studies the use of rate equations to analyse the cooling process in such systems. In particular the master equation is used to find rate equations that can determine the rate of change of phonons in the system. The general idea behind cavity cooling is the continuous conversion of phonons into cavity photons. While there is no spontaneous emission and decay rate associated with the concept of phonons, photons are created after a change in the phonon number has occurred and can then leak out through the cavity mirrors easily. Hence the conversion of phonons into photons can result in the constant removal of phonon energy from the system. In this thesis we compare cavity mediated cooling with single particle laser cooling. It is shown that cavity cooling is essentially the same as ordinary laser cooling. This is done by calculating the stationary state phonon number mss and the cooling rate y as a function of the system parameters. For example, when the trap phonon frequency υ is either much larger or much smaller than the cavity decay rate k , the minimum stationary state phonon number scales as k²/16v² (strong confinement regime) and as k/4 (weak confinement regime), respectively. Replacing k with Ѓ yields the steady states associated with ordinary laser cooling.
Cavity-mediated cooling has the potential to become one of the most efficient techniques to cool molecular species down to very low temperatures. In this paper we analyse cavity cooling with single-laser driving for relatively large cavity decay rates κ and relatively large phonon frequencies ν. It is shown that cavity cooling and ordinary laser cooling are essentially the same within the validity range of the Lamb–Dicke approximation. This is done by deriving a closed set of rate equations and calculating the corresponding stationary state phonon number and cooling rate. For example, when ν is either much larger or much smaller than κ, the minimum stationary state phonon number scales as κ2/16ν2 (strong confinement regime) and as κ/4ν (weak confinement regime), respectively.
Cavity-mediated cooling has the potential to become one of the most efficient techniques to cool molecular species down to very low temperatures. In this paper we analyse cavity cooling with single-laser driving for relatively large cavity decay rates kappa and relatively large phonon frequencies nu. It is shown that cavity cooling and ordinary laser cooling are essentially the same within the validity range of the Lamb-Dicke approximation. This is done by deriving a closed set of rate equations and calculating the corresponding stationary state phonon number and cooling rate. For example, when nu is either much larger or much smaller than kappa, the minimum stationary state phonon number scales as kappa^2/16 nu^2 (strong confinement regime) and as kappa / 4 nu (weak confinement regime), respectively.
The cooling rate for cavity-mediated laser cooling scales as the Lamb-Dicke parameter $\ensuremath{\eta}$ squared. A proper analysis of the cooling process hence needs to take terms up to ${\ensuremath{\eta}}^{2}$ in the system dynamics into account. In this paper, we present such an analysis for a standard scenario of cavity-mediated laser cooling with $\ensuremath{\eta}\ensuremath{\ll}1$. Our results confirm that there are many similarities between ordinary and cavity-mediated laser cooling. However, for a weakly confined particle inside a strongly coupled cavity, which is the most interesting case for the cooling of molecules, numerical results indicate that more detailed calculations are needed to model the cooling process accurately.
We analyze theoretically a one-dimensional model of laser cooling of an atom or ion trapped in a cavity. We assume that the cavity loss rate is much larger than the atom-cavity coupling (bad-cavity limit) and that the atomic excited state is weakly occupied (low saturation limit). After elimination of the cavity mode and the atomic excited state, we derive rate equations for the populations of the trap states. We find that in the Lamb-Dicke limit the atom can be cooled to the ground state of the trap even in the strong confinement limit. This result is interpreted in terms of quantum interferences between different cooling and heating processes involving spontaneous emission in the cavity.
Cooling is indispensable for trapping and observing single free atoms.In atomic physics, this can be achieved efficiently by laser cooling.Conventional methods to laser cool atoms are based on repeated optical pumping cycles followed by spontaneous emission of a photon from the atom.Such pumping schemes can only be applied to certain atomic species, which have a closed optical transition.Drawbacks caused by photons spontaneously emitted from the atom can be avoided in the strongly coupled atom-cavity system in which energy and entropy can be removed by photons lost from the cavity.This thesis reports on the first observation of this cooling mechanism which does not rely on spontaneous emission.In the experiment, a single atom is captured in an intracavity dipole trap.Illuminating the system with a weak, slightly blue-detuned light beam extends the storage time of the atom in the trap.The observed cooling force is at least five times larger than the force achieved by free-space cooling methods at comparable excitation of a two-level atom.Utilising cavity cooling, single atoms are prepared strongly-coupled to the mode of a high-finesse cavity.This allows to observe two well-resolved normal-mode peaks in both the cavity transmission as well as in the trap lifetime.The experiment is in agreement with a Monte Carlo simulation, demonstrating the localisation of the atom to within a tenth of a wavelength.The ability to individually excite the normal modes opens new possibilities to use this system for applications in quantum information science, including the realisation of quantum-logic gates.In the future cavity cooling might be applied to systems which cannot be cooled by conventional methods as for instance molecules or an atom carrying a quantum bit.
Here we analyze cavity-mediated laser cooling for an experimental setup with an external trap which strongly confines the motion of a particle in the direction of the cavity axis. It is shown that the stationary-state phonon number exhibits three sharp minima as a function of the atom-cavity detuning due to a direct atom-phonon-photon coupling term in the system Hamiltonian. These resonances have the same origin as the Mollow triplet in the resonance fluorescence of a laser-driven atomic system. It is shown that a laser-Rabi-frequency-dependent atom-cavity detuning yields the lowest stationary-state phonon number for a wide range of experimental parameters.