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Annual Meeting Optical Society of America

Squeezing with coupled pendulums: two-level atoms in a cavity

Mark G. Raizen, Luis A. Orozco, Min Xiao, Robert J. Brecha, H. Jeffrey Kimble

Published Jan 1, 1987• 0 citations
Publisher

Abstract

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.

DOI
10.1364/oam.1987.mq5

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Scientific Reports•Mar 30, 2017•13 citations
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.
Experiments to generate squeezed states of light are described for a collection of two-level atoms within a high-finesse cavity. The investigation is conducted in a regime for which the weak-field coupling of atoms to the cavity mode produces a splitting in the normal mode structure of the atom–field system that is large compared with the atomic linewidth. Reductions in photocurrent noise of 30% (−1.55 dB) below the noise level set by the vacuum state of the field are observed in a balanced homodyne detector. A degree of squeezing of approximately 50% is inferred for the field state in the absence of propagation and detection losses. The observed spectrum of squeezing extends over a very broad range of frequencies (~±75 MHz), with the frequency of best squeezing corresponding to an offset from the optical carrier given by the normal mode splitting.
A new regime for the generation of squeezed states of the electromagnetic field is described for a collection of atoms within a high-finesse cavity. The process responsible for squeezing is a coupling-induced splitting in the normal-mode structure of the atom-field system. A theoretical analysis is presented that predicts large degrees of squeezing for modest operating conditions. An experimental investigation of this regime has produced noise reductions of 30% relative to the vacuum noise level.
Squeezed state generation for a system of two-level atoms interacting with the field of a high-finesse cavity has been extensively discussed both experimentally and theoretically in recent years. Most theories describing these systems take the cavity field as a plane traveling wave for simplicity. With this assumption it is quite difficult to make quantitative comparisons between theory and recent experiments. However, by employing the formalism developed in Ref. 1, we are able to treat rather general spatial variations of the intracavity field subject to the constraint of the good-cavity limit of optical bistability. Squeezed state generation for the three particular examples of a plane-wave ring interferometer, a Gaussian-mode ring cavity, and a plane-wave field in a standing-wave interferometer are considered to illustrate the formalism. Somewhat surprisingly, in regimes for which the plane-wave theory predicts 50-70% squeezing (cooperatively C ~102–103), the standing-wave structure produces only modest reductions in the squeezing (a few percent), while the radial variations of the field reduce the squeezing by ~10%.
Optical bistability is reexamined as a candidate system for the generation of squeezed states of light. Previous analyses have concluded that significant squeezing can be achieved only in a rather extreme range of parameter space relative to current experimental capabilities and only over a restricted range of frequencies near the carrier.1 By contrast we have identified a new regime in which appreciable squeezing should be obtainable for rather modest operating conditions and without excessive demands on the stability of external control parameters. Following the treatment by Carmichael,2 we have conducted a theoretical search for optimal squeezing in optical bistability in the general case without adiabatic elimination of atomic or cavity variables. Our analysis is based on a linearization of the generalized Fokker-Planck equation for a system of N atoms coupled to a single mode of a high finesse cavity. For comparable atomic and cavity decay rates, there is a mode splitting in the eigenvalue structure of the system which is responsible for the vacuum field Rabi splitting. It is near the spectral features associated with these vacuum field Rabi sidebands that we find significant squeezing. The concepts of optimum squeezing as indicated by Mandel's Q parameter and by the spectrum of squeezing are discussed with reference to the various operating regimes in optical bistability.
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.
Squeezed states of light are a set of nonclassical states in which the quantum fluctuations of one quadrature component are reduced below the standard quantum limit. With less noise than the best stabilised laser sources, squeezed light is a key resource in the field of quantum technologies and has already improved sensing capabilities in areas ranging from gravitational wave detection to biomedical applications. In this work we propose a novel technique for generating squeezed states of a confined light field strongly coupled to a two-level system, or qubit, in the dispersive regime. Utilising the dispersive energy shift caused by the interaction, control of the qubit state produces a time-dependent change in the frequency of the light field. An appropriately timed sequence of sudden frequency changes reduces the quantum noise fluctuations in one quadrature of the field well below the standard quantum limit. The degree of squeezing and the time of generation are directly controlled by the number of frequency shifts applied. Even in the presence of realistic noise and imperfections, our protocol promises to be capable of generating a useful degree of squeezing with present experimental capabilities.