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Journal of Modern Optics

Dynamics of the Generation of the Pure Two-atom Squeezed State

Mohamed Ridza Wahiddin, Z. Ficek, Siew-Yoong Ng

Published Apr 1, 1995• 1 citation
Publisher

Abstract

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.

DOI
10.1080/713824420

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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.
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 relaxation process of a single two-level atom driven by an intense resonant coherent field is studied in the presence of a broadband squeezed vacuum field. Generalized forms for the self-field operator and the field-dependent damping coefficients are derived. In the steady state, positive atomic inversion (~5%) is shown for some range of the phase of the squeezed vacuum field. The squeezing-induced enhanced and asymmetric coherence (i.e.?non-zero dispersive atomic polarization) induces profound asymmetry in the side-bands of the Mollow fluorescent spectrum and the absorptive?dispersive spectra near the Rabi side-band frequencies. The case of two and three cooperative atoms, instead of a single atom, shows (i)?positive atomic inversion in the steady state for larger interval of the squeeze phase parameter and more enhanced extrema for the atomic polarization components and (ii) the extra side peaks in the fluorescent spectrum become asymmetric and of dispersive-like profile. Dressed-state analysis in the single-atom case with the field-dependent decay process in the presence of the squeezed vacuum field is presented and shows that the inequality of the (field-dependent) decay rates of the dressed states leads to more positive inversion in the dressed states as compared with the normal vacuum case.
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 influence of the dipole-dipole interaction on the final atomic state of a two-atom system driven by a coherent laser field and damped by a broad-band squeezed vacuum is discussed. It is shown that in the absence of a coherent laser field the final atomic state is independent of the dipole-dipole interaction and can be the pure two-atom squeezed state only if detuning of the squeezed vacuum field from atomic resonance is equal to zero. In the presence of a coherent laser field, the final atomic state depends on the dipole-dipole interaction. As the latter increases, the final atomic state shifts from a mixed state to the pure two-atom squeezed state. However, this happens only if the driving field and the squeezed field frequencies are tuned to the atomic transition frequency. For the driving field and the squeezed vacuum field frequencies detuned from atomic resonance the system decays into a mixed state irrespective of the dipole-dipole interaction between the atoms.
The behavior of a two-level atom confined within a cavity, pumped by an intense external field, and damped by a squeezed vacuum reservoir is studied. When the lowest squeezed quadrature of the vacuum is in phase with the pumping field, the relaxation time of the population inversion and of the polarization quadratures of the atom are appreciably enlarged, and hence the atom is decoupled from the reservoir. The effects of finite bandwidth of the squeezing are analyzed and it is shown that they can be used to improve the decoupling.
We studied the electromagnetically induced transparency, where the three-level atom of Λ-type is put in two statistically independent squeezed vacuums. We start from the master equation containing the decay of the atom to the squeezed vacuums, and solve the non-diagonal density matrix element analytically, finding that it is strongly dependent on the squeezing degree and the phase of the squeezed vacuum. There is also a dependence on the intensity and phase of the probe beam, which would not appear in the normal vacuum case. By coupling with squeezed vacuums, the atom would not only experience electromagnetically induced transparency and slow group velocity, but also induce a fast group velocity,backward group velocity and a gain in the probe light field. Besides, the absorption and gain can be modulated by the intensity of probe light.