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Journal of the Optical Society of America B

Quantum beats in spontaneous emission from two atoms in a detuned squeezed vacuum

Mariam Saad, K. T. Lim, Mohamed Ridza Wahiddin, Z. Ficek

Published Nov 1, 1997• 2 citations
Publisher

Abstract

The time evolution of the populations of the collective states of a two-atom system in a squeezed vacuum can exhibit quantum beats. We show that the effect appears only when the carrier frequency of the squeezed field is detuned from the atomic resonance. Moreover, we find that the quantum beats are not present for the case in which the two-photon correlation strength is the maximum possible for a field with a classical analog. We also show that the population inversion between the excited collective states, found for the resonant squeezed vacuum, is sensitive to the detuning and the two-photon correlations. For large detunings or a field with a classical analog there is no inversion between the collective states. Observation of the quantum beats or the population inversion would confirm the essentially quantum-mechanical nature of the squeezed vacuum.

DOI
10.1364/josab.14.002767

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The time evolution of the populations of the collective states of a two-atom system in a squeezed vacuum can exhibit quantum beats. We show that the effect appears only when the carrier frequency of the squeezed field is detuned from the atomic resonance. Moreover, we find that the quantum beats are not present for the case in which the two-photon correlation strength is the maximum possible for a field with a classical analog. We also show that the population inversion between the excited collective states, found for the resonant squeezed vacuum, is sensitive to the detuning and the two-photon correlations. For large detunings or a field with a classical analog there is no inversion between the collective states. Observation of the quantum beats or the population inversion would confirm the essentially quantum-mechanical nature of the squeezed vacuum.
The authors present analytical and numerical results for resonance fluorescence produced by a two-level atom damped by a broad-band squeezed vacuum. Previous theoretical analyses of this model have assumed that the laser frequency and the carrier frequency of the squeezed vacuum are equal. The authors introduce a non-zero detuning between the laser frequency and the carrier frequency while maintaining resonance between the laser frequency and atomic resonance. In the absence of the driving field there is a squeezing threshold: above threshold the decay rate of the atomic polarization can be reduced, and below threshold a squeezing-induced two peak spectrum and frequency shift, which is analogous to the Bloch-Siegert shift, are predicted. In the presence of the driving field, the spectrum is asymmetric for Rabi frequencies smaller or comparable to the detuning of the squeezed vacuum. A symmetric spectrum is obtained for large Rabi frequencies. An interpretation is predicted by means of a dressed-state analysis. The authors find that for not too large Rabi frequencies a remarkably large population inversion can be induced in the dressed states, even at exact resonance of the driving field, provided that the laser frequency and carrier frequency are detuned. Moreover, for detection times larger than the inverse detuning, the spectrum is insensitive to the phase between the driving field and the squeezed vacuum, in marked contrast to the case of no detuning.
Spontaneous emission from two-level atoms interacting with a squeezed vacuum field is examined, taking account of possible different interatomic separations. It is shown that the steady-state atomic population depends on whether the interatomic separations are comparable to or much smaller than the resonant wavelength. For the extended system the squeezed vacuum introduces a dependence of the atomic population on the interatomic separations. For large interatomic separations the atomic population is identical to that for the thermal field, which is the same for two independent atoms. For small interatomic separations the atomic population is higher than that for the thermal field. This is in contrast to the small-sample model in which the interatomic separation is ignored. In this case the final atomic population in the squeezed vacuum is the same as that for the independent atoms in the squeezed vacuum. Moreover, this population differs from that for the thermal field for which the atomic population is lower than that for the independent atoms. This difference is due to the interatomic correlations whose presence depends on whether the interatomic separation is or is not included. For the extended system the interatomic correlations are induced by the squeezed field and vanish for the thermal field. For the small-sample model, however, the interatomic correlations are induced by the thermal field and the squeezed vacuum changes these correlations in such a way that for the minimum-uncertainty squeezed states these correlations vanish. We also discuss the effect of the interatomic separation on the two-photon transitions and the normalized intensity correlation function in the two-atom system interacting with the squeezed vacuum field.
We study the effect of a broadband squeezed vacuum on the dynamics of a two-atom system driven by a near resonant laser field. We show that only in the absence of the driving field are the collective atomic levels selectively populated. Otherwise all collective atomic levels are populated independently of the initial conditions and time. Moreover, we show that the mode correlations, characteristics for the squeezed vacuum, induce a population inversion which, in contrast to the selective population of the collective levels, is not destroyed by the driving field. The stationary lineshapes for the two atomic transitions are also studied. We show that in the squeezed vacuum the population in the upper collective level can exhibit three distinct peaks centred at the frequencies omega 0 and omega 0 +or- Omega 12 , where omega 0 is the atomic transition frequency and Omega 12 is the dipole-dipole interaction potential. The central peak is induced by the mode correlations, whereas the sidebands are induced by the driving field and show a strong dependence on the relative phase between the squeezed vacuum and the driving field. The population in the intermediate level shows a distinct peak at the frequency omega 0 + Omega 12 , and holes at omega 0 and omega 0 - Omega 12 .
The appearance of quantum beats in a two-time second-order correlation function is discussed for the case of spontaneous emission from two nonidentical atoms. The atoms are separated by distances comparable with the resonance wavelength and have different transition frequencies and natural line widths. It is shown that quantum beats appear for nonidentical and identical atoms. In the latter case the dipole–dipole interaction between the atoms is a necessary condition for the appearance of quantum beats. Two mechanisms lead to quantum beats in the case of nonidentical atoms and such beats may appear even for independent atoms. The effect is similar to that of interference between independent beams.
ABSTRACT T 0.1 Significance of the Study This study provides a comprehensive theoretical and numerical investigation of light emission from a two-level atom interacting with a squeezed vacuum field. By devel oping a model based on the squeezed Jaynes–Cummings Hamiltonian and formulating atomic evolution via the master equation, the work establishes a framework for un derstanding how quantum squeezing modifies atomic dynamics. Analysis of popula tion inversion and emission characteristics shows that squeezing can enhance or inhibit spontaneous emission, accelerate population oscillations, and induce spectral narrow ing, while the second-order correlation function g(2)(τ) reveals photon antibunching and nonclassical statistics. The study further examines two-atom systems coupled to a common squeezed vacuum, highlighting steady-state entanglement and nonclassical correlations in quadrature variances, emphasizing the role of squeezing as a quantum resource. Overall, these findings provide insight into the influence of squeezed reser voirs on spontaneous emission, coherence, photon correlations, and entanglement, with important implications for quantum optics, precision spectroscopy, quantum metrology, and quantum information processing. Keywords: Master equation; Power spectrum; Quantum entanglement;Spontaneous emission; Squeezed vacuum; Two-level atom
Time evolution of a two-atom system damped by a broad-band squeezed vacuum is examined. We show that in the squeezed vacuum the collective atomic levels are no longer eigenstates of the system. Diagonalizing the density matrix of the system, we find new ‘dressed’ eigenstates of the system and show that the evolution of the population of the dressed states is characterized by three different relaxation times, two of them strongly modified by the squeezed correlations. We find that the effect of the squeezed vacuum on the system appears on a time-scale larger than the shortest relaxation time of the system, and the relaxation time of the system to the pure two-atom squeezed state is strongly dependent on the intensity N of the squeezed vacuum and increases with increasing N.