Squeezed states of the electromagnetic fieM are generated by degenerate parametric down conversion in an optical cavity. Noise reductions greater than 50% relative to the vacuum noise level are observed in a balanced homodyne detector. A quantitative comparison with theory suggests that the observed squeezing results from a field that in the absence of linear attenuation would be squeezed by greater then tenfold.

An improvement in precision beyond the limit set by the vacuum-state or zero-point fluctuations of the electromagnetic field is reported for the measurement of phase modulation in an optical interferometer. The experiment makes use of squeezed light to reduce the level of fluctuations below the shot-noise limit. An increase in the signal-to-noise ratio of 3.0 dB relative to the shot-noise limit is demonstrated, with the improvement currently limited by losses in propagation and detection and not by the degree of available squeezing.PACS numbers: 42.50.Dv, 07.60.Ly, 42.50.Kb The quantum nature of the electromagnetic field leads to limitations on the sensitivity of precision measurement of amplitude or phase changes of the field. The quantum fluctuations responsible for enforcing a lower limit on the "noise" in an optical experiment are succinctly expressed in terms of uncertainty products that follow from the commutation relations between conjugate field operators. The fundamental limit encountered in optical physics has been the so-called "shot-noise" limit (SNL), which represents a level of fluctuations for which the minimum uncertainty allowed by quantum mechanics is achieved for the uncertainty product and for which the variances for each of two conjugate operators are equal. This symmetric distribution of fluctuations is characteristic of the vacuum state of the field (zero-point fluctuations) or of a coherent state (approximated by a single-mode laser).Although the vacuum fluctuations of the field have been the practical limit on precision optical measurement, these fluctuations are of course not a limit in principle since quantum states with variance less than that of the vacuum state can be employed. In particular, the use of squeezed states to circumvent the SNL has been discussed for many years in the theoretical literature. 1 " 8 Squeezed states are characterized by a phase-dependent distribution of quantum fluctuations such that the dispersion in one of two quadrature components of the field drops below the level set by the vacuum state. In a measurement with squeezed light, the signal that one wishes to detect is encoded on the field variable with reduced fluctuations. The detection scheme is arranged to be largely insensitive to the increased fluctuations in the conjugate variable that are required by the uncertainty relation.In this Letter we report an experiment in which an improvement in the signal-to-noise ratio of 3.0 dB relative to the SNL has been achieved in an optical measurement with squeezed states. The experiment follows the work of Caves on precision interferometry 6 and employs squeezed light in a Mach-Zehnder interferometer for the detection of phase modulation in propagation along the two arms of the interferometer. 9 The observed increase in sensitivity in the experiment is currently limited by simple linear losses in propagation and detection, and not by the available degree of squeezing from our source. Thus one might anticipate that these rather modest initial results can be su...

Motivated by the Kronecker product approximation technique, we have developed a very simple method to assess the inseparability of bipartite quantum systems, which is based on a realigned matrix constructed from the density matrix. For any separable state, the sum of the singular values of the matrix should be less than or equal to $1$. This condition provides a very simple, computable necessary criterion for separability, and shows powerful ability to identify most bound entangled states discussed in the literature. As a byproduct of the criterion, we give an estimate for the degree of entanglement of the quantum state.

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.

We report the first experimental demonstration of two-photon correlated imaging with true thermal light from a hollow cathode lamp. The coherence time of the source is much shorter than that of previous experiments using random scattered light from a laser. A two-pinhole mask was used as object, and the corresponding thin lens equation was well satisfied. Since thermal light sources are easier to obtain and measure than entangled light it is conceivable that they may be used in special imaging applications.Although imaging is an old and well-studied topic and is of great importance in classical optics, it is now attracting new interest in quantum optics due to recent experiments on two-photon correlated imaging. The first such experiment was based on quantum entangled photon pairs from spontaneous parametric down conversion in a nonlinear crystal, and gave rise to the name "ghost" imaging, so called because an object in one optical beam could produce an image in the coincident counts with a detector placed in another beam [1]. This experiment led to other interesting theoretical and experimental studies and, furthermore, a debate on the question whether entanglement is a prerequisite for ghost imaging [2]. The possibility to perform correlated imaging with thermal light was first predicted by Gatti et al [4]. The first experiment with a classical light source that demonstrated "two photon" coincidence imaging was performed by Bennink et al. using a coherent laser beam split along two paths with detectors that measured finite laser pulses [3].The difference between quantum and classical coincidence imaging and the extent to which a classical light source can mimic a quantum one have been widely discussed by the groups of Shih [5,6], Boyd [7], Lugiato [4,8,9], Zhu [10, 11] and Wang [12]. Experimentally, Shih and collaborators first achieved ghost imaging with a pseudo-thermal light source, and introduced the concepts of "two-photon coherence" and "twophoton incoherence" imaging [13]. Gatti et al. obtained high resolution ghost imaging with thermal-like speckle light. However, in all these experiments the primary light source was a He-Ne laser, and the pseudo-thermal beam was obtained by passage through a rotating ground glass plate [14].Different from these experiments, we report the demonstration of a two-photon correlated imaging experiment using a true thermal light source.We employed a commercial rubidium hollow-cathode lamp [16] manufactured by the General Research Institute for Nonferrous Metals (China), which is the type commonly used in atomic absorption spectroscopy because of its sharp spectral linewidth. The lamp was powered by a direct current of 20mA in our experiments, and the resonance wavelength was 780nm. However, the actual linewidth of hollow-cathode lamps depends on the pressure, filament structure etc and varies from model to model. In our model the inner diameter of the cathode was 3mm. To estimate the coherence time of our lamp we first carried out a Hanbury Brown-Twiss (HBT) type experiment...