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arXiv:quant-ph/0611221 · Optics Express

Self ordering threshold and superradiant backscattering to slow a fast gas beam in a ring cavity with counter propagating pump

Carl F. Maes, János K. Asbóth, Helmut Ritsch

Published Jan 1, 2007• 6 citations
arXivHTMLPDF

Abstract

We study the dynamics of a fast gaseous beam in a high Q ring cavity counter propagating a strong pump laser with large detuning from any particle optical resonance. As spontaneous emission is strongly suppressed the particles can be treated as polarizable point masses forming a dynamic moving mirror. Above a threshold intensity the particles exhibit spatial periodic ordering enhancing collective coherent backscattering which decelerates the beam. Based on a linear stability analysis in their accelerated rest frame we derive analytic bounds for the intensity threshold of this selforganization as a function of particle number, average velocity, kinetic temperature, pump detuning and resonator linewidth. The analytical results agree well with time dependent simulations of the N-particle motion including field damping and spontaneous emission noise. Our results give conditions which may be easily evaluated for stopping and cooling a fast molecular beam.

DOI
10.1364/oe.15.006019

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We study the dynamics of a fast gaseous beam in a high Q ring cavity counter propagating a strong pump laser with large detuning from any particle optical resonance. As spontaneous emission is strongly suppressed the particles can be treated as polarizable point masses forming a dynamic moving mirror. Above a threshold intensity the particles exhibit spatial periodic ordering enhancing collective coherent backscattering which decelerates the beam. Based on a linear stability analysis in their accelerated rest frame we derive analytic bounds for the intensity threshold of this selforganization as a function of particle number, average velocity, kinetic temperature, pump detuning and resonator linewidth. The analytical results agree well with time dependent simulations of the N-particle motion including field damping and spontaneous emission noise. Our results give conditions which may be easily evaluated for stopping and cooling a fast molecular beam.
Based on a classical point particle description, we study light induced transverse collimation and phase space compression of a fast molecular beam traversing the crossover region of a high- Q optical cavity and a standing-wave laser beam. The molecules scatter pump laser light, far detuned from any molecular transition, into the resonant cavity mode. We show that despite a very small probability for this process for a single particle, collective enhancement can lead to significant transverse cooling and collimation above the self-organization threshold. The analytical formulae for this threshold derived from homogeneous one-dimensional (1D) models give surprisingly good estimates for the pulsed 3D case. We compare ring and standing wave cavity geometries and show that phase space compression can be achieved even for extremely small particle field coupling if compensated by a large density and pump power. In the vicinity of the critical point the compression time can be reduced by tailored seeding of the cavity mode or using a second buildup cavity for the pump field.
The collective dynamics of mobile scatterers and light in optical resonators generates complex behaviour. For strong transverse illumination a phase transition from homogeneous to crystalline particle order appears. In contrast, cold particles inside a single-side pumped ring cavity exhibit an instability towards bunching and collective acceleration called collective atomic recoil lasing (CARL). We demonstrate that by driving two orthogonally polarized counterpropagating modes of a ring resonator one realises both cases within one system. As a function of the two pump intensities the corresponding phase diagram exhibits regions in which either a generalized form of self-ordering towards a travelling density wave with constant centre-of-mass velocity or a CARL instability is formed. Time-dependent control of the cavity driving then allows to accelerate or slow down and trap a sufficiently dense beam of linearly polarizable particles.
We have identified a novel phase stability mechanism from the intracavity field-induced self-organization of a fast-moving molecular beam into travelling molecular packets in the bad cavity regime, which is then used to decelerate the molecular packets by feedback-controlled time-varying laser pumps to the cavity. We first applied the linear stability analysis to derive an expression for this self-organization in the adiabatic limit and show that the self-organization of the beam leads to the formation of travelling molecular packets, which in turn function as a dynamic Bragg grating, thus modulating periodically the intracavity field by superradiant scattering of the pump photons. The modulation encodes the position information of the molecular packets into the output of the intracavity field instantaneously. We then applied time-varying laser pumps that are automatically switched by the output of the intracavity field to slow down the molecular packets via a feedback mechanism and found that most of the molecules in the molecular packets are decelerated to zero central velocity after tens of stages. Our cavity-based deceleration proposal works well in the bad cavity regime, which is very different from the conventional cavity-based cooling strategies where a good cavity is preferred. Practical issues in realizing the proposal are also discussed.
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.
Cavity cooling of an atom works best on a cyclic optical transition in the strong coupling regime near resonance, where small-cavity photon numbers suffice for trapping and cooling. A straightforward application to the cooling of the translational motion of other polarizable particles without sharply defined two-level transitions (such as molecules) fails as optical pumping transfers the particle into uncoupled states. An alternative operation in the far-off-resonant regime generates only very slow cooling due to the reduced field-particle coupling. We suggest one can overcome this by using a strongly driven ring cavity operated in the sideband cooling regime. The dynamics can be mapped onto the optomechanics setup with a movable mirror and allows one to take advantage of a collectively enhanced field-particle coupling by large photon numbers. A linearized analytical treatment confirmed by full numerical quantum simulations predicts fast cooling despite the off-resonant small single-particle--single-photon coupling. Even ground-state translational cooling (in the external potential) can be obtained by tuning the cavity field close to the Anti-stokes sideband for sufficiently high trapping frequency. Numerical simulations show quantum jumps of the particle between the lowest two trapping levels, which can be directly and continuously monitored via scattered light intensity detection.
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.