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Physical Review A

Dipole-dipole interaction in squeezed vacua

Elena V. Goldstein, Pierre Meystre

Published May 1, 1996• 10 citations
Publisher

Abstract

We study the near-resonant dipole-dipole interaction between two atoms in a broadband squeezed vacuum. We show that this ``vacuum'' modifies the rate of spontaneous emission of the atoms so that it may depend not merely on their relative position, as is normally the case, but also on their center-of-mass position. The explicit form of this latter dependence is a function of the way squeezing is achieved. We also show that in contrast to the spontaneous decay rate, squeezed vacua do not modify the dipole-dipole potential between the atoms as compared to its usual form. Finally, we develop a Monte Carlo wave-function description of the interaction between atoms with an arbitrary internal structure and a squeezed vacuum and apply this formalism to the case of off-resonant excitation of the atoms. We find that in addition to the usual light shift, the squeezed vacuum results in an additional contribution to the effective potential governing the evolution of the atomic ground states. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.53.3573

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We study the near-resonant dipole-dipole interaction between two atoms in a broadband squeezed vacuum. We show that this ``vacuum'' modifies the rate of spontaneous emission of the atoms so that it may depend not merely on their relative position, as is normally the case, but also on their center-of-mass position. The explicit form of this latter dependence is a function of the way squeezing is achieved. We also show that in contrast to the spontaneous decay rate, squeezed vacua do not modify the dipole-dipole potential between the atoms as compared to its usual form. Finally, we develop a Monte Carlo wave-function description of the interaction between atoms with an arbitrary internal structure and a squeezed vacuum and apply this formalism to the case of off-resonant excitation of the atoms. We find that in addition to the usual light shift, the squeezed vacuum results in an additional contribution to the effective potential governing the evolution of the atomic ground states. \textcopyright{} 1996 The American Physical Society.
The well-known Purcell effect shows that the spontaneous decay rate of an emitter can be affected by the electromagnetic environment with which the emitters interact. One of the most famous and popular examples is the squeezed vacuum. Although the squeezed vacuum does not change the density of states of the electromagnetic modes, it can modify the decay rate as well as the dephasing rate of the emitters. The interaction between a single atom and the squeezed vacuum has been widely studied, while only a few publications deal with the multiple-atom system. Despite the fact that the dipole-dipole interaction induced by ordinary vacuum depends on the relative separation of atoms, there are only a few papers studying the impact of atomic separation in the squeezed vacuum. In this dissertation, we show that the interaction induced by the squeezed vacuum depends on the center of mass positions of the atoms, which is essentially different from that in the ordinary vacuum. We also illustrate how to choose the coordinate system to make the center of mass position reasonable and well-defined.\n \nAlthough the squeezed vacuum theory has been widely studied, it is impractical to generate a broadband squeezed vacuum reservoir which squeezes all modes in the 3-dimensional (3D) space. Recently, photon transport in a one-dimensional (1D) waveguide coupled to quantum emitters (well known as "waveguide-QED") has attracted much attention due to its possible applications in quantum device and quantum information. In contrast to the 3D case, squeezing in 1D is more experimentally feasible. Suppression of the spontaneous decay rate and the linewidth of the resonance fluorescence atom has been experimentally demonstrated in a 1D microwave transmission line coupled to a single artificial atom. However many-body interaction in a 1D waveguide QED system coupled to the squeezed vacuum has still not yet been studied. In this dissertation, we apply our theory to the 1D waveguide-QED system with the squeezed reservoir. Contrary to the traditional result that the dephasing rate of a single atom is a constant, our calculation shows that the dephasing rate is actually position-dependent. As the dipole-dipole interaction is involved in the atomic system, both the atomic separation and center of mass position have impacts on the decay rate, dephasing rate, and the emitted resonance fluorescence spectrum. Moreover, the stationary maximum entangled NOON state can be achieved if atomic transition frequency is resonant with the center frequency of the squeezed vacuum.\n \nIn light of the fact that two qubits can be treated as a whole to be a four level atomic system, we also study the dynamics of Ξ-type atoms driven by a squeezed vacuum. We get the interesting result that the atomic system’s steady state is a pure state, and a complete population inversion can occur when the coupling between the atomic dipole and the squeezed vacuum satisfy some certain conditions. We also mathematically prove that the steady state of a many-body system is nothing else but the direct product of that in the single atom case even when dipole-dipole interaction is involved.
In contrast to electromagnetic fields, matter-wave fields are intrinsically interacting due to the presence of atom-atom collisions. Hence, matter-wave optics becomes effectively nonlinear as soon as the atomic densities are high enough that collisions can no longer be ignored. The goal of this dissertation is to study selected aspects of atom optics under such conditions. Specifically, Chapter 2 studies the near-resonant dipole-dipole interaction between two atoms in tailored vacua. In contrast to spontaneous emission, whose rate is known to be influenced by the type of vacuum the atom interacts with, we find that the dipole-dipole potential is determined only by the free space vacuum and is not modified either by thermal or squeezed vacua. In addition in the far off-resonance regime we find that the squeezed vacuum results in an additional contribution to the effective potential governing the evolution of the atomic ground state. In the second part of the dissertation, which comprises Chapter 3, we then study several aspects of the many-body theory of atomic ultracold systems in situations where the nonlinearity arises due to the two-body dipole-dipole interaction. After a formal theoretical development we discuss the possibility of using atomic phase conjugation off Bose condensates as a diagnostic tool to access the spatial coherence properties and to measure the lifetime of the condensate. We argue that phase conjugation provides an attractive alternative to the optical methods of probing condensate proposed in the past. We further study the elementary excitations in a multicomponent Bose condensates and determine the quasi-particle frequency spectrum. We show that in that case interferences resulting from cross-coupling between the condensate components can lead to a reversal of the sign of the effective two-body interaction and to the onset of spatial instabilities.
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.
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 compute the near-resonant dipole-dipole interaction between atoms in a three-dimensional optical lattice. After a general derivation, we concentrate specifically on the case of a J=1/2\ensuremath{\rightarrow}J=3/2 off-resonant transition, in which case the excited electronic states can be adiabatically eliminated. We present in detail the spatial dependence of the resulting effective dipole-dipole potential, and discuss the physical origin of its anisotropy. In addition to impacting the center-of-mass motion of the atoms, the effective dipole-dipole potential can induce electronic transitions within one or both atoms. The symmetries of the matrix elements corresponding to these various mechanisms are also commented upon. \textcopyright{} 1996 The American Physical Society.
The authors investigate the dipole-dipole interaction role in the resonance fluorescence of two identical two-level atoms, which are confined to a region much smaller than the resonant wavelength and which are damped by a squeezed vacuum. The spectrum consists of seven or five lines, depending on the relative phase between the driving field and the squeezed vacuum, whereas the spectrum without the dipole-dipole interaction displays three lines. The widths of these lines depend on the parameters of the squeezed vacuum and can be subnatural or supernatural depending on the phase. The central line and additional sidebands at double the Rabi frequency can have intensities larger than in the normal vacuum but the intensities of lines at one Rabi frequency are always less than in the normal vacuum.