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Quantum Optics Journal of the European Optical Society Part B

Squeezing in a super-radiant state

W S Liu, Paolo Tombesi

Published Apr 1, 1991• 3 citations
Publisher

Abstract

The authors obtain the times to reach the super-radiant states starting from an initial atomic de-excited state or an initial atomic excited state with the field in a squeezed state and discuss a variety of the resulting squeezings in such super-radiant states.
DOI
10.1088/0954-8998/3/2/002

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In the present paper, we consider the interaction of a single mode radiation initially in a coherent state with an assembly of two two-level atoms in some different states using the Hamiltonian, H = ω(a+a + Sz)+g(a S+ + a+ S-) in the natural units, where a+ and a are the creation and annihilation operators for radiation, Sz, S± are the collective Dicke operators, g is the coupling constant, ω is the energy of the photons and energy difference between the two atomic levels. We solve it exactly. We study ordinary squeezing and amplitude-squared squeezing of radiation for the general operators, [Formula: see text] and Yθ=1/2(a2e-iθ+a+2eiθ), when atoms are fully excited, super-radiant or in the ground state. We get a large ordinary squeezing (nearly 88% squeezing) for the super-radiant atomic state, at a time, which is 0.451 of the first revival time, and this should be easily observable. We also get a large amplitude-squared squeezing (nearly 20%) at the time, which is about 0.033 of the first revival time. Variation of variances near their minima with coupling time gt, square root of mean photon number |α| and phase are also discussed.
Time-dependent (numerical) results are presented for super-radiant behaviour in the Dicke model of N a = 2, 3 atoms in a broad band squeezed vacuum. This concerns the fluctuations and the intensity of the fluorescent radiation as well as the atomic population inversion of the system with atoms initially in an atomic coherent state. In the steady state, and in the N a → ∞, we show that the ‘atomic’ Dicke model behaves like a ‘giant quantum oscillator’, in which the number of excited atoms asymptotically approaches the average number of photons in the resonant mode of the squeezed vacuum, just as in the thermally driven case.
An S-conserving theory of collective resonance fluorescence by NNN two-level atoms driven by a uniform strong field is presented. The detuning between field and atoms can be varied. A canonical transformation to dress the atoms by the driving field and Langevin equations for dressed operators are used to investigate the behavior of the system. For sufficiently large detuning the dressed atoms are shown to reach a steady state after a transient super-radiant-like decay in times short, compared with the long decay time which is attained on resonance and which is the same as the single-atom spontaneous-decay time. In the transient regime the parameters of the quasi-super-radiant decay are shown to vary with detuning and with the driving-field amplitude. Both the amplitude spectrum and the integrated intensity of the fluorescence field, emitted off resonance by the dressed atoms during the transient, are shown to bear pulselike traces of the quasi-super-radiant decay. The elastic components of the off-resonance amplitude spectrum at the end of the super-radiant-like transient are broadened with respect to resonance, and the integrated intensity exhibits a sudden transient decrease in an appropriate range of detuning, which has been given the name "superdarkening" and which disappears on resonance. After the steady-state regime is attained, the resonance intensity spectrum is shown to coincide with that obtained by other authors, while off resonance the inelastic lines are broadened in a super-radiant-like fashion.