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Physical Review A

Squeezed excitation in cavity QED: Experiment and theory

Q. A. Turchette, N. Ph. Georgiades, Christina J. Hood, Harry J. Kimble, A. S. Parkins

Published Nov 1, 1998• 76 citations

Abstract

One of the canonical questions in quantum optics is the nature of the radiative properties of an atom when the normal vacuum fluctuations of the electromagnetic reservoir are replaced by the asymmetric, reduced fluctuations of a squeezed vacuum. While the basic radiative linewidth-narrowing effect has been known for over a decade [C. W. Gardiner, Phys. Rev. Lett. 56, 1917 (1986)], experimental realizations with operationally definable definitive manifestations of the quantum nature of the squeezed reservoir have been largely lacking from subsequent investigations. This paper presents measurements on an experimentally realized atom--squeezed-light system, in which the squeezed-light output of a subthreshold optical parametric oscillator illuminates an atom strongly coupled to a high-finesse optical resonator. Transmission of a weak probe field incident on the atom-cavity system is investigated both theoretically and experimentally. Alteration of the transmitted probe spectrum has been observed, as has a transmission modulation that depends on the phase of the squeezed field relative to a saturating coherent field (displaced squeezing). In certain parameter regimes, properties unique to the quantum nature of the squeezed light have been identified in the theoretical treatment, but complications in the experiment prevent their unequivocal measure. It is found that the observed effects of the squeezed light are dramatically reduced relative to the predictions of an idealized theory. This is quantitatively attributed to the effects of atomic beam fluctuations and a simple modeling of the atomic beam as an additional loss mechanism in the theory leads to reasonable agreement with the data.

DOI: 10.1103/physreva.58.4056

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One of the canonical questions in quantum optics is the nature of the radiative properties of an atom when the normal vacuum fluctuations of the electromagnetic reservoir are replaced by the asymmetric, reduced fluctuations of a squeezed vacuum. While the basic radiative linewidth-narrowing effect has been known for over a decade [C. W. Gardiner, Phys. Rev. Lett. 56, 1917 (1986)], experimental realizations with operationally definable definitive manifestations of the quantum nature of the squeezed reservoir have been largely lacking from subsequent investigations. This paper presents measurements on an experimentally realized atom--squeezed-light system, in which the squeezed-light output of a subthreshold optical parametric oscillator illuminates an atom strongly coupled to a high-finesse optical resonator. Transmission of a weak probe field incident on the atom-cavity system is investigated both theoretically and experimentally. Alteration of the transmitted probe spectrum has been observed, as has a transmission modulation that depends on the phase of the squeezed field relative to a saturating coherent field (displaced squeezing). In certain parameter regimes, properties unique to the quantum nature of the squeezed light have been identified in the theoretical treatment, but complications in the experiment prevent their unequivocal measure. It is found that the observed effects of the squeezed light are dramatically reduced relative to the predictions of an idealized theory. This is quantitatively attributed to the effects of atomic beam fluctuations and a simple modeling of the atomic beam as an additional loss mechanism in the theory leads to reasonable agreement with the data.

We present a study of semiconductor cavity QED effects with squeezed light. We investigate the effects of external squeezed light produced by a subthreshold optical parametric down conversion on the quantum features of the cavity as well as output radiation in the presence of exciton-exciton scattering. It turns out that the width of the spectrum of the cavity field strongly depends on the degree of squeezing. This effect is observed both in weak- and strong-coupling regimes. Moreover, we show that the external squeezed light has a profound effect on the amount of squeezing of the output field.

A cavity QED system is analysed which duplicates the dynamics of a two-level atom in free space interacting exclusively with broadband squeezed light. We consider atoms in a three-or four-level Λ configuration coupled to a high-finesse optical cavity which is driven by a squeezed light field. Raman transitions are induced between a pair of stable atomic ground states via the squeezed cavity mode and coherent driving fields. An analysis of the reduced master equation for the atomic ground states shows that a three-level atomic system has insufficient parameter flexibility to act as an effective two-level atom interacting exclusively with a squeezed reservoir. However, the inclusion of a fourth atomic level, coupled dispersively to one of the two ground states by an auxiliary laser field, introduces an extra degree of freedom and enables the desired interaction to be realized. As a means of detecting the reduced quadrature decay rate of the effective two-level system, we examine the transmission spectrum of a weak coherent probe field incident upon the cavity. The extension to multiple atoms is also considered and we show that such a cavity QED system may also duplicate the dynamics of an ensemble of two-level atoms collectively coupled to broadband squeezed light.

The experiments discussed in this thesis focus on the interaction of a single trapped atom with the single mode of a high-finesse optical cavity, in the regime of strong coupling. Chapter 1 gives a brief introduction, after which Chapter 2 describes our recent measurements of the transmission spectrum of the atom-cavity system. The spectrum exhibits a clearly resolved vacuum-Rabi splitting, in good quantitative agreement with theoretical predictions. A new Raman scheme for cooling atomic motion along the cavity axis enables a complete spectrum to be recorded for an individual atom trapped within the cavity mode, in contrast to all previous measurements of this type that have required averaging over 10^3-10^5 atoms. Chapter 3 discusses our observations of photon blockade for the transmitted light in the presence of one trapped atom. Excitation of the atom-cavity system by a first photon blocks the transmission of a second one, thereby converting an incident Poissonian stream of photons into a sub-Poissonian, anti-bunched stream, as confirmed by measurements of the photon statistics of the transmitted field. The intensity correlations of the cavity transmission also reveal the energy distribution for oscillatory motion of the trapped atom. Chapter 4 details a set of simple but necessary measurements of relevant experimental parameters such as cavity geometry, linewidth, mirror properties, birefringence, and detection efficiency. The thesis concludes with Appendix A, describing the efficient laser setup we use for our magneto-optical traps.

The system consisting of a two-level atom coupled strongly to a cavity mode behaves as a two-state system when excited near one of the ``vacuum'' Rabi resonances. With finite-bandwidth squeezed light incident upon the cavity and tuned to one of these resonances, we show that it is possible to realize a two-state system coupled to a squeezed vacuum. This system exhibits subnatural linewidths in the emitted spectra, as described by Gardiner [Phys. Rev. Lett. 56, 1917 (1986)] in a study of spontaneous emission of a two-level atom in a squeezed vacuum, but requires that only a single cavity mode be subject to squeezing rather than the entire three-dimensional vacuum.

Two-photon excitation of a three-level atom in a ladder configuration $(\stackrel{\ensuremath{\rightarrow}}{1}\stackrel{\ensuremath{\rightarrow}}{2}3)$ by simultaneous illumination with fields in squeezed vacuum and coherent states results in quantum interference for the excitation process. The particular configuration considered here is one for which the signal and idler output fields of a subthreshold nondegenerate optical parametric oscillator are in resonance with the two-stepwise dipole atomic transitions $(\stackrel{\ensuremath{\rightarrow}}{1}2,\stackrel{\ensuremath{\rightarrow}}{2}3),$ while a ``reference oscillator'' field is in two-photon resonance with the quadrupole transition $(\stackrel{\ensuremath{\rightarrow}}{1}3).$ In an extension of the work of Ficek and Drummond [Phys. Rev. A 43, 6247 (1991)], a theoretical formulation based on the full quantum master equation for the problem is presented. The combined effects of quantum interference and the nonclassical character of the squeezed state are investigated, and offer the potential for a new detection strategy for quantum fluctuations of the electromagnetic field with ultrahigh frequencies (10's--100's THz). Based on the theory developed, we analyze quantum interference in excitation in several special cases relevant to experimental realizations, including the effects of a small focusing angle of the squeezing onto the atoms, and unusual population inversions. Special emphasis is given to identifying intrinsically quantum optical field effects versus classical field effects. Procedures that could distinguish between the two (i.e., classical and nonclassical) are suggested.

A theoretical and experimental investigation of the generation of squeezed states of light has been carried out for a system of two-level atoms inside a high-finesse cavity. The regime that we consider is such that the coupling of atoms to the cavity mode produces a splitting in the normal mode structure of the atom-field system (the so-called vacuum-field Rabi splitting). We have employed this splitting to generate squeezing with observed reductions in photocurrent noise of 30 % below the shot-noise level. A degree of squeezing of ~50% is inferred for the field state in the absence of propagation and detection losses. Squeezing has been observed in two different cavity geometries with quite different coupling coefficients. In each case, the frequency of best squeezing corresponds to that of the normal mode splitting g N (g= single atom coupling coefficent and N = number of atoms) in good agreement with our theoretical predictions. Regions of parameter space with very large degrees of squeezing (>20×) are identified. Preliminary extensions of the theory into a transient regime with (cavity lifetime) ≪ (interaction time) ≪ (atomic lifetime) are described.