H. J. Kimble

Squeezed states of light from an optical parametric oscillator

Squeezed states of the electromagnetic field are generated by degenerate parametric downconversion in a subthreshold optical parametric oscillator. Reductions in photocurrent noise greater than 60% (-4 dB) below the limit set by the vacuum fluctuations of the field are observed in a balanced homodyne detector. A quantitative comparison with theory suggests that the observed noise reductions result from a field that in the absence of avoidable linear attenuation would be squeezed more than tenfold. A degree of squeezing of approximately fivefold is inferred for the actual field emitted through one mirror of the optical parametric oscillator. An explicit demonstration of the Heisenberg uncertainty principle for the electromagnetic field is made from the measurements, which show that the field state produced by the downconversion process is a state of minimum uncertainty.

Squeezed-state generation in optical bistability

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.

Detection of amplitude modulation with squeezed light for sensitivity beyond the shot-noise limit

An improvement in precision beyond the limit set by the vacuum-state or zero-point fluctuations of the electromagnetic field is reported for the detection of amplitude modulation encoded on a weak signal beam. The improvement is achieved by employing the squeezed light from an optical parametric oscillator to reduce the level of fluctuations below the shot-noise limit. An increase in signal-to-noise ratio of 2.5 dB relative to the shot-noise limit is demonstrated.

Interference effects in second-harmonic generation within an optical cavity

An experiment is described that investigates certain interference effects for second-harmonic generation within a resonant cavity. By employing a noncollinear geometry, the phases of two fundamental beams from a frequency-stabilized dye laser can be controlled unrestricted by the boundary conditions imposed in an optical cavity containing a KDP crystal and resonant at the second harmonic. The fundamental beams are either traveling or standing waves and generate either one or two coherent sources of ultraviolet radiation within the cavity. The experiment demonstrates explicitly the dependence of second-harmonic phase on the fundamental phases and the dependence of coupling efficiency on the overlap of the harmonic polarization wave with the cavity-mode function. The measurements agree well with a simple theory.

Observation of oscillatory energy exchange in a coupled-atom-cavity system

Observations of the oscillatory exchange of excitation between N two-state atoms and a single mode of a high-finesse optical cavity are reported in a regime of weak-field excitation and of comparable atomic and cavity damping rates. The observed frequencies of oscillation, approximately given by g√N, where g is the single-photon Rabi frequency, are in reasonable agreement with theoretical predictions.

Squeezed-state generation for two-level atoms in a spatially varying field mode

A spatially varying field mode is included in calculating the squeezing effect for a system of two-level atoms in the good-cavity limit. Two examples of a Gaussian mode field in a ring cavity and a plane-wave field in a standing-wave interferometer are used to demonstrate the quite general method. In qualitative terms, the squeezing predicted for plane waves is preserved. However, for a given value of atomic cooperativity parameter C, there is a degradation in squeezing because of the spatially varying field structure.

Intracavity Frequency Doubling for the Generation of Squeezed States of Light

While squeezed states of light represent a manifestation of the nonclassical character of the electromagnetic field and hence are of great intrinsic interest in quantum optics, there are as well a number of applications in measurement science associated with the possibility of sensitivity beyond the standard quantum limit. Given the landmark initial observation of this phenomenon by Slusher et al. [1], a number of experimental groups are concentrating on making their own “first” observations and on subsequently exploring limitations on the degree of achievable and detectable squeezing [2,3]. Most of the experimental research thus far has concentrated on squeezing produced by four-wave mixing, either in atomic vapors or in condensed media. The tack that we have taken is to investigate a completely different technique with a new set of potential advantages (and disadvantages). Our experiments attempt to produce squeezed states of light by second harmonic generation within an optical cavity resonant at both fundamental and harmonic frequencies. Of course the Hamiltonian describing the two-mode coupled system in the limit of a lossless medium is related to a broad class analyzed by Yuen[4], and hence it is not surprising that squeezing is predicted in this system. However, an issue that is of prime importance in our investigation is the extent to which these parametric models of quantized nonlinear processes are realistic. This issue is naturally entangled with a number of other technological and scientific questions that we are only beginning to unravel. We begin in Section II with an overview of the relevant theoretical predictions before turning in Section III to the actual experiment. Other contributions to this volume as well as review articles [5] should be consulted for a more comprehensive view of the field.

Optical Bistability with Two-State Atoms: Steady States and Dynamical Instabilities

A fundamental problem in optical physics is the interaction of two-level atoms with the electromagnetic field of a resonant cavity. Our experiments [1] with two-state sodium atoms are directed towards a quantitative investigation of the steady-state characteristics, dynamical behavior and the quantum statistical nature of the atom-field interaction in such a system. We report absolute comparisons between experiment and the single-mode theory of optical bistability with a Gaussian transverse profile.

Experimental Investigation of the Single-Mode Instability in Optical Bistability

Instabilities in optical systems form a very rich and exciting field of work.1 A great deal of theoretical effort has been devoted to understanding the complex behavior observed in the experiments. Active optical systems such as the laser have attracted more attention than passive systems; among the latter, the driven cavity filled with a collection of two-state atoms represents a canonical system in optical physics.2 Its study has shown optical bistability, instabilities, higher-order dynamical states and non-classical quantum statistics of the transmitted field.3

Generation and Application of Squeezed States of Light

Squeezed states of light have recently been generated in several laboratories by a variety of techniques [1]. As the name implies, squeezed states are states for which the variance in one of two quadrature phase amplitudes is reduced (squeezed) below the level associated with the zero-point or vacuum fluctuations of the electromagnetic field [2]. Because of an uncertainty relation constraining the product of variances, this reduction is necessarily accompanied by an increase in fluctuations above the vacuum level for the orthogonal quadrature-phase amplitude. Squeezed states are of great intrinsic interest from the perspective of quantum optics because of the nonclassical nature of the radiation field in these states. There is as well a growing interest in the potential that squeezed states offer for improvements in the precision of optical measurements and for fundamental spectroscopic investigations. In this brief contribution we review the research program at the University of Texas at Austin relating to the generation and application of squeezed states.