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Journal of Physics B Atomic Molecular and Optical Physics

Optical forces on a two-level atom in a broadband squeezed vacuum

S. V. Lawande, Padmakar V. Panat

Published Jun 8, 2004• 1 citation
Publisher

Abstract

An expression for dipolar and dissipative forces is obtained for a two-level atom with squeezed ground state. The atom is exposed to a coherent beam of frequency ωL with the spatial cross-sectional profile and Guoy phase . In our model, we assume that the broadband squeezed vacuum has a line width larger than that of a transition from a state |2 to a state |1 of the two-level atom. Moreover, we assume that the squeezed band is centred around ωL. Our expressions for the optical forces reduce to the standard expressions when the squeezing parameter goes to zero. We use an appropriate master equation for the reduced density operator with the squeezed vacuum bath. A steady-state solution of the density operator ρ is obtained to evaluate π12 and π21 which are required to find optical forces. We also obtain the time evolution of the dipolar force and the dissipative force in an intense field limit. We have shown that the dipolar force in a squeezed vacuum is non-conservative and non-zero even if the detuning parameter is zero.

DOI
10.1088/0953-4075/37/12/012

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An expression for dipolar and dissipative forces is obtained for a two-level atom with squeezed ground state. The atom is exposed to a coherent beam of frequency ωL with the spatial cross-sectional profile and Guoy phase . In our model, we assume that the broadband squeezed vacuum has a line width larger than that of a transition from a state |2 to a state |1 of the two-level atom. Moreover, we assume that the squeezed band is centred around ωL. Our expressions for the optical forces reduce to the standard expressions when the squeezing parameter goes to zero. We use an appropriate master equation for the reduced density operator with the squeezed vacuum bath. A steady-state solution of the density operator ρ is obtained to evaluate π12 and π21 which are required to find optical forces. We also obtain the time evolution of the dipolar force and the dissipative force in an intense field limit. We have shown that the dipolar force in a squeezed vacuum is non-conservative and non-zero even if the detuning parameter is zero.
The master equation for a two-level atom interacting with a strong coherent field and damped into a reservoir formed by a finite bandwidth squeezed vacuum is derived. The master equation extends the Yeoman and Barnett approach to a non-zero detuning of the driving field from the atomic resonance and allows to discuss the role of squeezing bandwidth and the detuning in the level shifts, widths and intensities of spectral lines. The approach is valid for arbitrary values of the Rabi frequency and detuning but for the squeezing bandwidths larger than the natural linewidth in order to satisfy the Markov approximation.
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.
A complete treatment of a three-level ladder system interacting with a broadband squeezed vacuum field is presented. It is assumed that the ground state and the second excited state are decoupled in the electric-dipole approximation, and are tuned close to the sum frequency of the incident squeezed vacuum field. Using Zwanzig's projection-operator techniques, we derive the master equation, assuming that the system interacts with a broadband squeezed vacuum field in one or more dimensions. It is shown that, in the first case, the squeezed vacuum introduces new decay constants and frequency-shift parameters. These have the same dependence on the atom-radiation coupling parameter as the ordinary vacuum decay rate and frequency shift, the only major difference being that they are multiplied by the squeezing parameters M and N. In more dimensions, the decay constants and frequency-shift parameters depend on the solid angle \ensuremath{\Omega} over which the squeezing is propagated. For \ensuremath{\Omega}=0 these correspond to the usual Einstein A coefficients and Lamb shifts of the atomic levels, while for large \ensuremath{\Omega} they are similar to those for the one-dimensional squeezed vacuum.
We study fluorescence from a three-level atom in a cascade configuration driven by two coherent fields and damped by a broadband squeezed vacuum. Under the conditions that one or both of these fields are intense, a secular approximation is invoked to derive an analytical solution of the relevant master equation. When the two fields are in exact resonance with their respective transitions, expressions for the fluorescent spectra show a narrowing of the central peak for some specific values of the parameters of the squeezed vacuum and the phases between the driving fields and the squeezed vacuum. We also present analytical expressions for second-order intensity correlations. The inhibition of fluorescence in a squeezed vacuum is reflected in the quantum-jump-like behavior shown by these correlations.
If a broadband squeezed vacuum is treated as a reservoir with respect to a two-level atom, the non-zero phase-dependent reservoir correlation functions characterizing the squeezed vacuum introduce `squeezing terms' to the master equation. These terms are responsible, for example, for the well known narrowing of the spectral lines in the resonance fluorescence spectrum of the atom. For a squeezed vacuum reservoir with finite bandwidth it is possible to derive the master equation that is consistent with the Born-Markov approximation by a two-step procedure which consists in dressing the atom first and next coupling it to the finite-bandwidth reservoir. The master equation is valid whenever the bandwidth of the reservoir is much broader than the atomic linewidth but not necessarily broader than the Rabi frequency. This procedure can be applied not only for the squeezed vacuum reservoir but also for the ordinary vacuum with the structure of the mode density that is not flat, e.g., modelled by a Lorentzian function as in a cavity. The master equation for this case, in the operator form, shows some similarities to the master equation for the squeezed vacuum reservoir due to the presence of the `squeezing-like terms'. The similarities and differences of the two master equations are discussed in this paper.
We report exact results concerning the effect of dipole-dipole interaction (dispersion forces) on dynamic and steady-state characteristics of squeezing in the emitted fluorescent field from two identical coherently driven two-level atoms. The atomic system is subjected to three different damping baths in particular the normal vacuum, a broad band thermal field and a broad band squeezed vacuum. The atomic model is the Dicke model, hence possible experiments are most likely to agree with theory when performed on systems of Rydberg atoms making microwave transitions. The presence of dipole-dipole interaction can enhance squeezing for realizable values of the various parameters involved.