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arXiv:1401.4961 · New Journal of Physics

Cavity cooling of an atomic array

O. S. Mishina

Published Mar 19, 2014• 10 citations
arXivHTMLPDF

Abstract

While cavity cooling of a single trapped emitter was demonstrated, cooling of many particles in an array of harmonic traps needs investigation and poses a question of scalability. This work investigates the cooling of a one dimensional atomic array to the ground state of motion via the interaction with the single mode field of a high-finesse cavity. The key factor ensuring the cooling is found to be the mechanical inhomogeneity of the traps. Furthermore it is shown that the pumped cavity mode does not only mediate the cooling but also provides the necessary inhomogeneity if its periodicity differs from the one of the array. This configuration results in the ground state cooling of several tens of atoms within a few milliseconds, a timescale compatible with current experimental conditions. Moreover, the cooling rate scaling with the atom number reveals a drastic change of the dynamics with the size of the array: atoms are either cooled independently, or via collective modes. In the latter case the cavity mediated atom interaction destructively slows down the cooling as well as increases the mean occupation number, quadratically with the atom number. Finally, an order of magnitude speed up of the cooling is predicted as an outcome the optimization scheme based on the adjustment of the array versus the cavity mode periodicity.

DOI
10.1088/1367-2630/16/3/033021

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While cavity cooling of a single trapped emitter was demonstrated, cooling of many particles in an array of harmonic traps needs investigation and poses a question of scalability. This work investigates the cooling of a one dimensional atomic array to the ground state of motion via the interaction with the single mode field of a high-finesse cavity. The key factor ensuring the cooling is found to be the mechanical inhomogeneity of the traps. Furthermore it is shown that the pumped cavity mode does not only mediate the cooling but also provides the necessary inhomogeneity if its periodicity differs from the one of the array. This configuration results in the ground state cooling of several tens of atoms within a few milliseconds, a timescale compatible with current experimental conditions. Moreover, the cooling rate scaling with the atom number reveals a drastic change of the dynamics with the size of the array: atoms are either cooled independently, or via collective modes. In the latter case the cavity mediated atom interaction destructively slows down the cooling as well as increases the mean occupation number, quadratically with the atom number. Finally, an order of magnitude speed up of the cooling is predicted as an outcome the optimization scheme based on the adjustment of the array versus the cavity mode periodicity.
We show that an ensemble of two-level atoms commonly coupled to a single, driven, damped high-QQQ cavity mode could be cooled and trapped via the correlated dynamics of cavity field and the atomic motion. For sufficiently large detuning between the atoms and the field, spontaneous emission plays no role in the dynamics, and the cooling scheme can be applied to all particles with a sufficient optical dipole moment. The time scale of this collective cooling process increases with the particle number and can be optimized by suitably tailoring the pump field amplitude and frequency. The key properties of the underlying mechanism are discussed using a linearized model, where one can derive a closed set of equations for certain ensemble averages and the field. The results are then compared with N-particle dynamical simulations of the full equations.
We theoretically analyze the cooling dynamics of an atom which is tightly trapped inside a high-finesse optical resonator. Cooling is achieved by suitably tailored scattering processes, in which the atomic dipole transition either scatters a cavity photon into the electromagnetic field external to the resonator, or performs a stimulated emission into the cavity mode, which then dissipates via the cavity mirrors. We identify the parameter regimes in which the atom center-of-mass motion can be cooled into the ground state of the external trap. We predict that, in particular, for high cooperativities, interference effects mediated by the atomic transition may lead to higher efficiencies. The dynamics is compared with the cooling dynamics of a trapped atom inside a resonator studied by Zippilli and Morigi [Phys. Rev. Lett. 95, 143001 (2005)] where the atom, instead of the cavity, is driven by a laser field.
Cavity quantum electrodynamic system with strongly coupled single atoms provides a good platform for studying quantum information processing, quantum simulation, quantum network, and distributed quantum computing. Cooling and trapping single atoms is a crucial technique in the quantum technology. At present, in a high-finesse cavity with finite space, cooling and trapping single atoms is a big challenge, even though it is a mature technique for free space. Great efforts have been made to cool and trap single atoms inside a cavity, and for a trapped atom its lifetime has reached as long as tens of seconds. Developing a more flexible method of cooling and trapping single atoms in a cavity is still essential for a strongly coupled cavity quantum electrodynamic system. In this work, we demonstrate experimentally that a single cesium atom in a cavity can be trapped by utilizing a single optical tweezer settled in cavity mode, and its lifetime is (2.60 ± 0.18) s. The experiment is carried out in a Fabry-Perot cavity, which is assembled by two concave mirrors each with a curvature radius of 100 mm, and cavity length of 335 μm. The concave surfaces are highly reflective, and the cavity has a finesse of 6.1 × 104. The 1080 nm optical tweezer with a waist of 2 μm is formed by an achromatic lens group with a numerical aperture of 0.4. At first, the precooled atomic assemble released from the magneto-optical trap (MOT) is transferred into cavity mode by an optical dipole trap with a waist of 36 μm. Then, one of the successfully transferred atoms is captured by the optical tweezer with the aid of cavity cooling mechanism. A blue detuned cavity locking laser is used as a standing-wave optical trap along the cavity axis. The signal of successfully trapped one atom is obtained by recording transmission of the cavity that will decrease owing to the strong coupling induced vacuum Rabi splitting. Finally, we demonstrate the precise manipulation of the atom-cavity coupling strength, which is achieved by scanning the position of the trapped atom step by step by using a high-precision translation stage. The system realized in this work can be used to study the dynamics of single atom-photon interactions with adjustable coupling strength. In addition, the mechanism adopted in this work is compatible with constructing tweezer arrays inside cavity mode, and thus possesses more flexibility and great potentials in cavity-based quantum entanglement and quantum simulation.
Cavity-mediated cooling of the center--of--mass motion of a transversally, coherently pumped atom along the axis of a high--Q cavity is studied. The internal dynamics of the atomic dipole strongly coupled to the cavity field is treated by a non-perturbative quantum mechanical model, while the effect of the cavity on the external motion is described classically in terms of the analytically obtained linear friction and diffusion coefficients. Efficient cavity-induced damping is found which leads to steady-state temperatures well-below the Doppler limit. We reveal a mathematical symmetry between the results here and for a similar system where, instead of the atom, the cavity field is pumped. The cooling process is strongly enhanced in a degenerate multimode cavity. Both the temperature and the number of scattered photons during the characteristic cooling time exhibits a significant reduction with increasing number of modes involved in the dynamics. The residual number of spontaneous emissions in a cooling time for large mode degeneracy can reach and even drop below the limit of a single photon.
In this thesis we investigate the dynamics of cold atoms in optical cavities. We study how the scattering properties of laser driven atoms are modified by the presence of an optical resonator. This investigation can be divided into two parts. First, we study the scaling of the scattering properties with the number of atoms, and we show in particular how Bragg scattering by an atomic lattice is modified by the presence of the resonator. In this case, the atoms are trapped at the antinodes of the cavity mode function by the mechanical potential induced by the resonator. In a second part, we show how this modification of the scattering properties can be used for efficiently cooling single atoms to the ground state of a harmonic trap. In particular, we find that the motion is critically affected by quantum correlations induced by the mechanical coupling with the resonator, which may lead to selective suppression of certain transitions for the appropriate parameters regimes, thereby increasing the cooling efficiency.
We study the laser cooling of one atom in a harmonic trap beyond the Lamb-Dicke regime. By using sequences of laser pulses of different detunings we show that the atom can be confined into just one state of the trap, either the ground state or an excited state of the harmonic potential. The latter can be achieved because under certain conditions an excited state becomes a dark state. We study the problem in one and two dimensions. For the latter case a different cooling mechanism is possible, based on the destructive interference between the effects of laser fields in different directions, which allows the creation of a variety of dark states. For both, one- and two-dimensional cases, Monte Carlo simulations of the cooling dynamics are presented.