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arXiv:0902.3366 · Physical Review A

Recoil-induced subradiance in an ultracold atomic gas

Mary M. Cola, D. Bigerni, N. Piovella

Published May 14, 2009• 23 citations
arXivHTMLPDF

Abstract

Subradiance, i.e., the cooperative inhibition of spontaneous emission by destructive interatomic interference, can be realized in a cold atomic sample confined in a ring cavity and lightened by a two-frequency laser. The atoms, scattering the photons of the two laser fields into the cavity mode, recoil and change their momentum. Under proper conditions the atomic initial momentum state and the first two momentum recoil states form a three-level degenerate cascade. A stationary subradiant state is obtained after the scattered photons have left the cavity, leaving the atoms in a coherent superposition of the three collective momentum states. Both a semiclassical description of the process and the quantum subradiant state with its Wigner function are given. Antibunching, quantum correlations, and entanglement between the atomic modes of the subradiant state are demonstrated.

DOI
10.1103/physreva.79.053622

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•Dec 11, 2018•0 citations
Subradiance, i.e., the cooperative inhibition of spontaneous emission by destructive interatomic interference, can be realized in a cold atomic sample confined in a ring cavity and lightened by a two-frequency laser. The atoms, scattering the photons of the two laser fields into the cavity mode, recoil and change their momentum. Under proper conditions the atomic initial momentum state and the first two momentum recoil states form a three-level degenerate cascade. A stationary subradiant state is obtained after the scattered photons have left the cavity, leaving the atoms in a coherent superposition of the three collective momentum states. Both a semiclassical description of the process and the quantum subradiant state with its Wigner function are given. Antibunching, quantum correlations, and entanglement between the atomic modes of the subradiant state are demonstrated.
This paper is the first of a sequence of four papers devoted to the theoretical study of subradiance, i.e. of the cooperative inhibition of spontaneous emission, a phenomenon which has been recently observed. It is shown, in the typical example of a pencil-shaped sample of three-level atoms in the 'V' configuration (two transitions sharing a common lower level), that the system can spontaneously reach a state in which the emission in the so-called 'end-fire' superradiant field modes is cooperatively inhibited; this occurs for initially uncorrelated atoms when the initial state is a statistical mixing of the two upper states. The whole study is centered on the concept of destructive interatomic interference and it is therefore based on the symmetry properties of the collective atomic state with respect to the permutations of locally indistinguishable atoms. Semiclassical and fully quantum-mechanical models are used in turn. The obstacles to the interatomic interference and thus to subradiance are finally discussed.
We experimentally investigate the formation of subradiant atomic momentum states in Bose-Einstein condensates inside a recoil resolving optical ring resonator according to the theoretical proposal of Cola, Bigerni, and Piovella. The atoms are pumped from the side with laser light that contains two frequency components. They resonantly drive cavity assisted Raman transitions between three discreet atomic momentum states. Within a few hundred microseconds, the system evolves into a stationary subradiant state. In this state, the condensate develops two density gratings suitable to diffract the two frequency components of the pump field into the resonator. Both components destructively interfere such that scattering is efficiently suppressed. A series of subradiant states for various amplitude ratios of the two pump components between 0 and 2.1 have been observed. The results are well explained with a three state quantum model in mean field approximation.
We demonstrate that superradiance and collective atomic recoil lasing from cold atoms can be enhanced using a two-frequency pump with frequency difference twice the two-photon recoil frequency ${\ensuremath{\omega}}_{r}$. In the good-cavity regime the atoms behave as a three-recoil-level system, collectively scattering a single-frequency radiation mode. In the bad-cavity regime, the superradiant cascade through the different recoil momentum states is strongly accelerated. The emitted radiation shows a discrete spectrum whose harmonics are separated by $2{\ensuremath{\omega}}_{r}$ and generated by transitions between adjacent momentum levels.
For pt.I see ibid., vol.18, p.3811 (1985). This paper is the second of a theoretical study of subradiance, i.e. of the cooperative inhibition of spontaneous emission by a destructive interatomic interference, a phenomenon which has recently been observed. It is devoted to the particular case of atomic systems with degenerate transitions, i.e. with several transitions of the same frequency and the same polarisation. The interatomic interference which then occurs between the different transitions is responsible, when destructive, for a new sort of subradiance. The phenomenon is studied for a few typical level configurations, using both quantum mechanical and semiclassical models. The first example concerns a four-level configuration with two transitions of the same frequency and polarisation. The other examples concern three-level configurations with a degenerate transition; in the case of the 'degenerate' cascade, new superradiant beats and subradiance effects are predicted.
For pt.II see ibid., vol.19, p.2109 (1986). This paper is the third in a theoretical study of subradiance, i.e. the cooperative inhibition of spontaneous emission by a destructive interatomic interference, a phenomenon which has recently been observed. The paper is devoted to the problem of the cooperative spontaneous emission of atomic samples with linear dimensions much smaller than the wavelength of the emitted light. The treatment, which is based on a fully quantum mechanical description of the problem, corroborates the results obtained in a semiclassical treatment by Friedberg and Hartmann (1974). Starting from a master equation describing both the cooperative spontaneous emission and the dipole-dipole interaction, a statistical treatment of the latter is introduced and the corresponding symmetry relaxation is studied. The evolution of the atoms is described in three typical cases that correspond to different sample geometries and/or atomic distributions. In one of these cases, in particular, the symmetry is first conserved and the atoms follow Dicke's predictions for a time. A 'retarded' symmetry breaking then occurs suddenly, near the zero value of the collective energy, as in Friedberg and Hartmann's calculations for a small sphere. With regard to the further evolution of the atoms in this case, which cannot be studied in a semiclassical model, it is shown that the decay rate quickly becomes much smaller than the incoherent decay rate. An unquestionable subradiance phenomenon is thus predicted in this case.
The problem of the interaction of N atoms with a laser beam and vacuum modes can give rise to many interesting phenomena concerning the spontaneous emission of light and its propagation in the medium. The cooperative effects, for example, such as superadiance and subradiance, are effects related to the coherence created between the atoms when a photon is emitted spontaneously by a single excited atom. Superradiance can be defined as the enhancement of the spontaneous emission due to constructive interference of the scattered light. Its counterpart, subradiance, is the trapping of some remaining light due to destructive interference. In cold atoms, some previous theoretical works predict and characterize these two cooperative effects in a large and diluted atomic cloud, in the regime of low intensities and large detunings of the incident laser. The theoretical model is a coupled-dipole model for two-level atoms driven by a low-intensity field and in the scalar approach. The experiment consists in measuring the super- and subradiant decay rates from the temporal emitted intensity after the switch off of the incident laser in the steady state. Our experimental setup consists in a magneto-optical trap of rubidium 87 atoms at large resonant optical thicknesses. A probe beam excites the atoms close to the D2 line. The intensity emitted is detected by a single photon detector with no afterpulsing and a calibration procedure allows us to determine the resonant optical thickness of the cloud and its temperature. In this work, we report the experimental observation of super- and subradiance in a large cloud of cold atoms. For subradiance, the main result is the linear evolution of the characteristic time with the resonant optical thickness of the cloud and its independence of the detuning. For superradiance, we observe superradiance out of the forward direction. We verify the validity of our interpretations with the predictions of the coupled-dipole model. Finally, we discuss the interplay of subradiance and radiation trapping, as well as theoretical predictions for: a setup of a phased cloud, to control the subradiant amplitude emission; and temperature effects, where subradiance is shown to be robust in a large range of temperatures.