Semiclassical theory of cavity-assisted atom cooling (original) (raw)
Related papers
Cavity cooling of a single atom
Nature, 2004
All conventional methods to laser-cool atoms rely on repeated cycles of optical pumping and spontaneous emission of a photon by the atom. Spontaneous emission in a random direction is the dissipative mechanism required to remove entropy from the atom. However, alternative cooling methods have been proposed 1, 2 for a single atom strongly coupled to a high-finesse cavity; the role of spontaneous emission is replaced by the escape of a photon from the cavity. Application of such cooling schemes would improve the performance of atom cavity systems for quantum information processing 3, 4 . Furthermore, as cavity cooling does not rely on spontaneous emission, it can be applied to systems that cannot be laser-cooled by conventional methods; these include molecules 2 (which do not have a closed transition) and collective excitations of Bose condensates 5 , which are destroyed by randomly directed recoil kicks. Here we demonstrate cavity cooling of single rubidium atoms stored in an intracavity dipole trap. The cooling mechanism results in extended storage times and improved localization of atoms. We estimate that the observed cooling rate is at least five times larger than that produced by free-space cooling methods, for comparable excitation of the atom.
Laser-driven atom moving in a multimode cavity: strong enhancement of cavity-cooling efficiency
2002
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.
Scaling properties of cavity-enhanced atom cooling
Physical Review A, 2001
We extend an earlier semiclassical model to describe the dissipative motion of N atoms coupled to M modes inside a coherently driven high-finesse cavity. The description includes momentum diffusion via spontaneous emission and cavity decay. Simple analytical formulas for the steady-state temperature and the cooling time for a single atom are derived and show surprisingly good agreement with direct stochastic simulations of the semiclassical equations for N atoms with properly scaled parameters. A thorough comparison with standard free-space Doppler cooling is performed and yields a lower temperature and a cooling time enhancement by a factor of M times the square of the ratio of the atom-field coupling constant to the cavity decay rate. Finally it is shown that laser cooling with negligible spontaneous emission should indeed be possible, especially for relatively light particles in a strongly coupled field configuration.
04 03 03 3 v 1 3 M ar 2 00 4 Cavity cooling of a single atom
All conventional methods to laser-cool atoms rely on repeated cycles of optical pumping and spontaneous emission of a photon by the atom. Spontaneous emission in a random direction is the dissipative mechanism required to remove entropy from the atom. However, alternative cooling methods have been proposed 1, 2 for a single atom strongly coupled to a high-finesse cavity; the role of spontaneous emission is replaced by the escape of a photon from the cavity. Application of such cooling schemes would improve the performance of atom cavity systems for quantum information processing 3, 4. Furthermore, as cavity cooling does not rely on spontaneous emission, it can be applied to systems that cannot be laser-cooled by conventional methods; these include molecules 2 (which do not have a closed transition) and collective excitations of Bose condensates 5 , which are destroyed by randomly directed recoil kicks. Here we demonstrate cavity cooling of single rubidium atoms stored in an intracavity dipole trap. The cooling mechanism results in extended storage times and improved localization of atoms. We estimate that the observed cooling rate is at least five times larger than that produced by free-space cooling methods, for comparable excitation of the atom.
Photon cooling by dispersive atom-field coupling with atomic postselection
arXiv: Quantum Physics, 2019
We propose, in a Ramsey interferometer, to cool the cavity field to its ground state, starting from a thermal distribution by a dispersive atom-field coupling followed by an atomic postselection. We also analyze the effect of the cavity and atomic losses. The proposed experiment can be realized with realistic parameters with high fidelity.
Cold atoms in cavity-generated dynamical optical potentials
Reviews of Modern Physics, 2013
We review state-of-the-art theory and experiment of the motion of cold and ultracold atoms coupled to the radiation field within a high-finesse optical resonator in the dispersive regime of the atom-field interaction with small internal excitation. The optical dipole force on the atoms together with the back-action of atomic motion onto the light field gives rise to a complex nonlinear coupled dynamics. As the resonator constitutes an open driven and damped system, the dynamics is non-conservative and in general enables cooling and confining the motion of polarizable particles. In addition the emitted cavity field allows for real-time monitoring of the particle's position with minimal perturbation up to sub-wavelength accuracy. For many-body systems, the resonator field mediates controllable long-range atom-atom interactions, which set the stage for collective phenomena. Besides correlated motion of distant particles, one finds critical behavior and non-equilibrium phase transitions between states of different atomic order in conjunction with superradiant light scattering. Quantum degenerate gases inside optical resonators can be used to emulate opto-mechanics as well as novel quantum phases like supersolids and spin glasses. Non-equilibrium quantum phase transitions as predicted by e.g. the Dicke Hamiltonian can be controlled and explored in real-time via monitoring the cavity field. In combination with optical lattices, the cavity field can be utilized for non-destructive probing Hubbard physics and tailoring long-range interactions for ultracold quantum systems.
Feedback cooling of atomic motion in cavity QED
Physical Review A, 2006
We consider the problem of controlling the motion of an atom trapped in an optical cavity using continuous feedback. In order to realize such a scheme experimentally, one must be able to perform state estimation of the atomic motion in real time. While in theory this estimate may be provided by a stochastic master equation describing the full dynamics of the observed system, integrating this equation in real time is impractical. Here we derive an approximate estimation equation for this purpose, and use it as a drive in a feedback algorithm designed to cool the motion of the atom. We examine the effectiveness of such a procedure using full simulations of the cavity QED system, including the quantized motion of the atom in one dimension.
Quantum dynamics of cavity-assisted photoassociation of Bose-Einstein-condensed atoms
Physical Review A, 2009
We explore the quantum dynamics of photoassociation of Bose-Einstein condensed atoms into molecules using an optical cavity field. Inside of an optical resonator, photoassociation of quantum degenerate atoms involves the interaction of three coupled quantum fields for the atoms, molecules, and the photons. The feedback created by a high-Q optical cavity causes the cavity field to become a dynamical quantity whose behavior is linked in a nonlinear manner to the atoms inside and where vacuum fluctuations have a more important role than in free space. We develop and compare several methods for calculating the dynamics of the atom-molecule conversion process with a coherently driven cavity field. We first introduce an alternate operator representation for the Hamiltonian from which we derive an improved form of mean field theory and an approximate solution of the Heisenberg-Langevin (HL) equations that properly accounts for quantum noise in the cavity field. It is shown that our improved mean field theory corrects several deficiencies in traditional mean field theory based on expectation values of annihilation/creation operators. Also, we show by direct comparison to numerical solutions of the density matrix equations that our approximate quantum solution of HL equations gives an accurate description of weakly or undriven cavities where mean field theories break down.
Physical Review A, 1999
We investigate the photon statistics of the light transmitted from a driven optical cavity containing N two-level atoms, with emphasis on the weak driving field limit. This limit is of most interest from the point of view of quantum fluctuations. We find that various types of nonclassical behavior are possible, even with large numbers of atoms in the cavity, under conditions of strong atom-field coupling, which we refer to as the cavity quantum electrodynamics limit. We describe the system with a pure-state formalism valid for weak fields, and also use a Fokker-Planck equation obtained by a small fluctuation linearization. We examine the conditions under which the linearized theory is appropriate, and explore the sensitivity of nonclassical effects in the system to atom number, transit-time broadening, and detunings. ͓S1050-2947͑99͒04803-9͔
Shaking' of an atom in a non-stationary cavity
Physics Letters A, 2000
We consider an atom interacting with a quantized electromagnetic field inside a cavity with variable parameters. The atom in the ground state located in the initially empty cavity can be excited by variation of cavity parameters. We have discovered two mechanisms of atomic excitation. The first arises due to the interaction of the atom with the non-stationary electromagnetic field created by modulation of cavity parameters. If the characteristic time of variation of cavity parameters is of the order of the atomic transition time, the processes of photon creation and atomic excitation are going on simultaneously and hence excitation of the atom cannot be reduced to trivial absorption of the photons produced by the dynamical Casimir effect. The second mechanism is "shaking" of the atom due to fast modulation of its ground state Lamb shift which takes place as a result of fast variation of cavity parameters. The last mechanism has no connection with the vacuum dynamical Casimir effect. Moreover, it opens a new channel of photon creation in the non-stationary cavity. Nevertheless, the process of photon creation is altered by the presence of the atom in the cavity, even if one disregards the existence of the new channel. In particular, it removes the restriction for creation of only even number of photons and also changes the expectation value for the number of created photons. Our consideration is based on a simple model of a two-level atom interacting with a single mode of the cavity field. Qualitatively our results are valid for a real atom in a physical cavity.