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Collective quantum dynamics ofanatomic lattice coupled toanoptical resonator

Stefano Zippilli, Giovanna Morigi, János K. Asbóth, Helmut Ritsch

Published Jan 1, 2005• 0 citations

Abstract

We study thequantum dynamics ofanarray ofcoherently driven two-level atomscoupled toanoptical resonator. The setupt isdepicted inthefigure [1]. Inthestrong coupling regime thecavity field generated byatomic scattering interferes destructively withthepumpontheatoms. Inthis configuration atomic excitation issuppressed evenforstrong driving fields, while thestationary intracavity field amplitude isalmost independent oftheatomnumber. Themagnitude ofthis interference effect depends onthedetuning between laser andcavity field andontherelative atomic positions andis strongest whentheatoms areordered inawavelength spaced lattice placed attheantinodes ofthecavity mode. Inthis case three dimensional intensity minima arecreated inthevicinity ofeachatom[1]. Weanalyze themechanical forces inthe regime wheretheinterference condition isfulfilled, andshowthat theatomic pattern ismechanically stable whenever the driving frequency isreddetuned withrespect tothecavity frequency, irrespective oftheatomic transition frequency. Hence atomic self organization, aspredicted in[2]canalso occurintheparameter regime wheresuperradiant scattering is suppressed bycollective interference. Wediscuss howthese results giveanewkeytounderstand recent experiments oncollective cavity cooling andmayallow toimplement fast tailored atom-atom interactions aswellasnonperturbative particle detection withverysmall energy transfer. I -_~~

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We study thequantum dynamics ofanarray ofcoherently driven two-level atomscoupled toanoptical resonator. The setupt isdepicted inthefigure [1]. Inthestrong coupling regime thecavity field generated byatomic scattering interferes destructively withthepumpontheatoms. Inthis configuration atomic excitation issuppressed evenforstrong driving fields, while thestationary intracavity field amplitude isalmost independent oftheatomnumber. Themagnitude ofthis interference effect depends onthedetuning between laser andcavity field andontherelative atomic positions andis strongest whentheatoms areordered inawavelength spaced lattice placed attheantinodes ofthecavity mode. Inthis case three dimensional intensity minima arecreated inthevicinity ofeachatom[1]. Weanalyze themechanical forces inthe regime wheretheinterference condition isfulfilled, andshowthat theatomic pattern ismechanically stable whenever the driving frequency isreddetuned withrespect tothecavity frequency, irrespective oftheatomic transition frequency. Hence atomic self organization, aspredicted in[2]canalso occurintheparameter regime wheresuperradiant scattering is suppressed bycollective interference. Wediscuss howthese results giveanewkeytounderstand recent experiments oncollective cavity cooling andmayallow toimplement fast tailored atom-atom interactions aswellasnonperturbative particle detection withverysmall energy transfer. I -_~~

We study the quantum dynamics of an array of coherently driven two-level atoms coupled to an optical resonator. In the strong coupling regime the cavity field generated by atomic scattering interferes destructively with the pump on the atoms. In this configuration atomic excitation is suppressed even for strong driving fields, while the stationary intracavity field amplitude is almost independent of the atom number. The magnitude of this interference effect depends on the detuning between laser and cavity field and on the relative atomic positions and is strongest when the atoms are ordered in a wavelength spaced lattice placed at the antinodes of the cavity mode. In this case three dimensional intensity minima are created in the vicinity of each atom. We analyze the mechanical forces in the regime where the interference condition is fulfilled, and show that the atomic pattern is mechanically stable whenever the driving frequency is red detuned with respect to the cavity frequency, irrespective of the atomic transition frequency

When N driven atoms emit in phase into a high-Q cavity mode, the intracavity field generated by collective scattering interferes destructively with the pump driving the atoms. Hence atomic fluorescence is suppressed and cavity loss becomes the dominant decay channel for the whole ensemble. Microscopically, 3D light-intensity minima are formed in the vicinity of the atoms that prevent atomic excitation and form a regular lattice. The effect gets more pronounced for large atom numbers, when the sum of the atomic decay rates exceeds the rate of cavity losses and one would expect the opposite behavior. These results provide new insight into recent experiments on collective atomic dynamics in cavities.

We theoretically investigate the correlated dynamics of N coherently driven atoms coupled to a standing-wave cavity mode. For red detuning between the driving field and the cavity as well as the atomic resonance frequencies, we predict a light force induced self-organization of the atoms into one of two possible regular patterns, which maximize the cooperative scattering of light into the cavity field. Kinetic energy is extracted from the atoms by superradiant light scattering to reach a final kinetic energy related to the cavity linewidth. The self-organization starts only above a threshold of the pump strength and atom number. We find a quadratic dependence of the cavity mode intensity on the atom number, which demonstrates the cooperative effect.

In a recent paper Meyer and Yeoman [Phys. Rev. Lett. 79, 2650 (1997)] have shown that the resonance fluorescence from two atoms placed in a cavity and driven by an incoherent field can produce an interference pattern with a dark center. We study the fluorescence from two coherently driven atoms in free space and show that this system can also produce an interference pattern with a dark center. This happens when the atoms are in nonequivalent positions in the driving field, i.e., the atoms experience different intensities and phases of the driving field. We discuss the role of the interatomic interactions in this process and find that the interference pattern with a dark center results from the participation of the antisymmetric state in the dynamics of the driven two-atom system.

We study the classically driven two-level system with its center-of-mass motion vibrating in a harmonic trap and coupled to the photons in a two-mode cavity. The first mode is resonant to the driving field and an electronic transition. The second mode is off-resonant, forming a vibrational-assisted Raman transition. Using an exact numerical method, we investigate the quantum dynamics of the light emitted by the atom and the cavity modes. We analyze and compare the corresponding atomic and intracavity photon spectra for a range of the driving laser field and the cavity coupling strengths. The results provide better understanding of the effects of the laser field and atom-cavity coupling strengths on quantum interference effects and photon blockade, particularly the Mollow's triplet and the Autler-Townes splitting in the good and bad cavity limits.

We investigate the behaviour of the intracavity field in a strongly coupled atom–cavity system (a collection of two-level atoms inside a high-Q cavity) driven by a short strong external resonant pulse. A new effect is predicted, the amplification of the intracavity field appears if the atomic number density in a cavity exceeds the instability threshold which is proportional to the square of the strong driving field. The amplification gain is proportional to the amplitude of the strong driving field. The amplitude of the intracavity field in the vicinity of a critical point above the threshold is time-dependent modulated with harmonics of half of the Rabi frequency of the driving field.