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Laser cooling of quantum systems

Javier Cerrillo Moreno

Published Jan 1, 2012• 0 citations
Publisher

Abstract

In this thesis novel methods for the laser cooling of quantum systems are presented. The use of quantum interference allows for the tailored cancelation of heating processes, so that an approximation to a cooling operator is possible that does not rely on the rotating wave approximation. This makes these schemes considerably faster and more efficient than existing ground state cooling methods, and allow for a significant relaxation of current experimental constraints. Several approaches are investigated in different systems. On the one hand, a special laser configuration, applicable to trapped ions, atoms or cantilevers, generates a double dark state that eliminates both the blue sideband and the carrier transition. As a consequence, vanishing phonon occupation up to first order in the perturbative expansion is achieved. Underlying this scheme is a combined action of two cooling schemes which makes the proposal very stable under parameter fluctuations. Its suitability as a cooling scheme for several ions in a trap or for a cloud of atoms in a dipole trap is shown. On the other hand, a pulsed cooling scheme for optomechanical systems is presented. It can be implemented for both strongly and weakly coupled optomechanical systems in both weakly and highly dissipative cavities. Its underlying mechanism is based on interferometric control of optomechanical interactions, and its efficiency is demonstrated with pulse sequences that are obtained by using methods from optimal control. Finally, it is shown how this pulsed method can be combined with continuous measurement to drive mechanical oscillators to highly squeezed steady states. Its mechanism relies on the modification of the dissipation and measurement terms, which drive the system towards a specific quadrature eigenstate. The scheme is robust to measurement inefficiencies and works also with highly dissipative cavities, which makes it accessible to implementation with state of the art technology.

DOI
10.25560/12788

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In this thesis novel methods for the laser cooling of quantum systems are presented. The use of quantum interference allows for the tailored cancelation of heating processes, so that an approximation to a cooling operator is possible that does not rely on the rotating wave approximation. This makes these schemes considerably faster and more efficient than existing ground state cooling methods, and allow for a significant relaxation of current experimental constraints. Several approaches are investigated in different systems. On the one hand, a special laser configuration, applicable to trapped ions, atoms or cantilevers, generates a double dark state that eliminates both the blue sideband and the carrier transition. As a consequence, vanishing phonon occupation up to first order in the perturbative expansion is achieved. Underlying this scheme is a combined action of two cooling schemes which makes the proposal very stable under parameter fluctuations. Its suitability as a cooling scheme for several ions in a trap or for a cloud of atoms in a dipole trap is shown. On the other hand, a pulsed cooling scheme for optomechanical systems is presented. It can be implemented for both strongly and weakly coupled optomechanical systems in both weakly and highly dissipative cavities. Its underlying mechanism is based on interferometric control of optomechanical interactions, and its efficiency is demonstrated with pulse sequences that are obtained by using methods from optimal control. Finally, it is shown how this pulsed method can be combined with continuous measurement to drive mechanical oscillators to highly squeezed steady states. Its mechanism relies on the modification of the dissipation and measurement terms, which drive the system towards a specific quadrature eigenstate. The scheme is robust to measurement inefficiencies and works also with highly dissipative cavities, which makes it accessible to implementation with state of the art technology.
A detailed study of a robust and fast laser cooling scheme on a three level system is presented. A special laser configuration, applicable to trapped ions, atoms or cantilevers, designs a quantum interference that eliminates the blue sideband in addition to the carrier transition, thus excluding any heating process involving up to one-phonon processes. As a consequence cooling achieves vanishing phonon occupation up to first order in the Lamb-Dicke parameter expansion. Underlying this scheme is a combined action of two cooling schemes which makes the proposal very stable under fluctuations of the physical parameters such as laser intensity or detuning, making it a viable candidate for experimental implementation. Furthermore, it is considerably faster than existing ground state cooling schemes, overcoming one of the limitations of current quantum information processing implementations. Its suitability as a cooling scheme for several ions in a trap or for a cloud of atoms in a dipole trap is shown.
We present a detailed analysis of a robust and fast laser cooling scheme [J. Cerrillo et al., Phys. Rev. Lett. 104, 043003 (2010)] on a three-level system. A special laser configuration, applicable to trapped ions, atoms, or cantilevers, designs a double-path quantum interference that eliminates the blue sideband in addition to the carrier transition, thus excluding any heating process involving up to one-phonon interactions. As a consequence, cooling achieves vanishing phonon occupation up to first order in the Lamb-Dicke parameter expansion. Underlying this scheme is a combined action of two cooling schemes which makes the proposal very flexible under constraints of the physical parameters such as laser intensity, detuning, or optical access, making it a viable candidate for experimental implementation. Furthermore, it is considerably faster than existing ground state cooling schemes. Its suitability as a cooling scheme for several ions in a trap and three-dimensional cooling is shown.
This thesis concentrates on generating and measuring non-classical states of mechanical oscillators by coupling them to atomic and molecular quantum systems. We start with a discussion of what novel physics can be explored by mechanical systems operating in the quantum regime. We then discuss one technique making it a possibility- cavity optomechanics, particularly optomechanical cooling. We investigate the limits of optomechanical cooling and review how the coupling of mechanical oscillators to external heat baths limits the minimum attainable phonon occupation number. As a possible alternative for circumventing clamping losses, we consider an all-optical approach where the mechanical element (in this case, a Bragg mirror) is suspended via optical forces, and discuss some limitations of this approach. We explore several schemes aimed at the generation of quantum states in mechanical oscillators. We consider specifically two examples: one in which the mechanical oscillator is coupled to polar molecules via dipole-dipole interaction, and another where it is magnetically coupled to a Bose condensate. The first example emphasizes that such an interaction can generate parametric squeezing and entanglement. The second scheme demonstrates that the back action of BEC spin measurements can be used to generate quantum states of motion of a mechanical oscillator. We then discuss possible methods for measuring the entire density matrix of a mechanical oscillator. The first method achieves the tomographic reconstruction of the mechanical Wigner function by coupling it simultaneously to a classical optical oscillator and a qubit. The second approach involves a state transfer scheme between momentum excitations of a bose-condensate in a cavity and a moving mirror of the cavity that is entirely mediated by the light field. We conclude with a discussion of the broader implications of this work, and some future research directions.
Cooling down a trapped ion into its motional ground state is a central step for trapped-ion-based quantum information processing. State-of-the-art cooling schemes often work under a set of optimal cooling conditions derived analytically using a perturbative approach, in which the sideband coupling is assumed to be the weakest of all the relevant transitions. As a result, the cooling rate is severely limited. Here we propose to use a quantum control technique powered with automatic differentiation to speed up the classical cooling schemes. We demonstrate the efficacy of our approach by applying it to find the optimal cooling conditions for classical sideband cooling and electromagnetically induced transparency cooling schemes, which are in general beyond the weak-sideband-coupling regime. Based on those numerically found optimal cooling conditions, we show that faster cooling can be achieved while at the same time a low average phonon occupation can be retained.