Nondegenerate Parametric Oscillator Research Articles

Photon-counting statistics of the subthreshold nondegenerate parametric oscillator.

Statistics of photons emitted by a nondegenerate parametric oscillator (NDPO) operating below threshold are discussed. Analytical expressions for the generating function are obtained when two non degenerate modes of the NDPO are mixed on a photocathode or when the intensities of the two modes are added. From the generating function, photon-counting distributions and waiting-time distributions as measured by a detector placed outside the cavity are derived

Quantum noise reduction in the squeezed pump non-degenerate parametric oscillator

The authors present a simple quantum model of the non-degenerate parametric oscillator above threshold where the pump has squeezed fluctuations. Quantum noise reduction is predicted not only for the signal and idler beams intensity difference, but also for the intensity sum. For pumps with greatly reduced intensity fluctuations, near perfect squeezing is also predicted for the individual signal and idler intensities.

Properties of a quantum light amplifier in a high-Q cavity, applied to a nondegenerate parametric oscillator

An ideal linear quantum light amplifier (QLA) in a highly reflecting cavity is considered and the conditions for realizing the best possible noise properties of such a device are obtained. These results are applied to a cavity nondegenerate parametric amplifier (NDPO). Approximating the pump mode of the NDPO as a classical field, the NDPO is an ideal linear amplifier. This behavior is quantitatively shown to be modified by the quantum fluctuations of the pump mode.

Pump fluctuations, phase mismatch, and detuning from resonances in the formation of quantum states of a nondegenerate resonant parametric oscillator

The evolution of quantum fields in a three-resonator optical parametric oscillator is analyzed. It is shown that the frequencies of the emitted waves may be stabilized if the influence of the phase mismatch is compensated by suitable changes in the optical length of the resonator. Spectra of the signal intensity fluctuations are calculated and investigated taking into account various destabilizing factors.

Nondegenerate four-wave mixing in a cavity: instabilities and quantum noise reduction

Abstract We consider the four-wave mixing interaction of three longitudinal cavity modes in a unidirectional ring cavity containing a system of two-level atoms. The set of equations which governs the dynamics of the system coincides with that of multimode optical bistability, and describes the behaviour of the system over all its parameter space. We identify an appropriate limit in which the model reduces exactly to a parametric interaction among the three modes. In this limit the model is fully quantum mechanical and it includes all the physical processes that are relevant in the limit (four-wave mixing, phase modulation, cross phase modulation). The stationary solutions of the parametric model are calculated analytically and display a complex scenario, which includes also the possibility of undamped oscillations of the modal amplitudes. Using the parametric model we calculate analytically also the spectrum of the fluctuations of the intensity difference between the signal fields, above the threshold of generation of the signals. It turns out that this coincides with the expression of the spectrum that is well known in the case of the nondegenerate parametric oscillator.

Intensity fluctuations in a frequency down-conversion process with three-level atoms.

An ideal nondegenerate parametric oscillator is known to give perfect squeezing in the difference of the intensities of the signal and idler modes. In this paper, we look at a frequency down-conversion system comprising three-level atoms in a cavity. The squeezing in the intensity difference is calculated and found, in general, to be degraded by spontaneous emission. In the limit of large detunings, the system is found to behave as a nondegenerate parametric oscillator.

Mutual quantum fluctuations of modes in the case of two-mode parametric oscillation in a resonator

A quantum solution of the problem of two-mode nondegenerate parametric oscillation in a resonator cavity with an arbitrary Q factor is proposed. It is shown that the existing semiclassical analysis is unsatisfactory. If the signal and idler modes are photodetected independently, the noise level in the normalized spectrum of the difference photocurrent is independent of the parametric gain increment. There are optimal Q factors of the resonator for different frequencies in this spectrum.

Commutation relations and laser linewidth.

The waves reflected from a resonator must obey the commutation relations of waves in free space. This fact alone, regardless of whether the medium in the resonator is linear or nonlinear, imposes commutation relations on the internal noise sources. The minimum linewidth of an oscillator can be derived from this fact alone. This paper analyzes the special cases of a nondegenerate parametric oscillator and diode laser oscillator and shows how the physical noise sources satisfy the commutation relations and how the linewidth is determined from them.

Correlations in nondegenerate parametric oscillation. II. Below threshold results.

We develop the quantum theory of a driven, damped intracavity parametric oscillator in the case of nondegenerate signal and idler modes. An analysis of the results of different types of local-oscillator measurements on the outgoing modes is presented. The frequency-domain squeezing is calculated below threshold including the effect of detunings and nonequal decay rates. We also calculate a nonclassical correlation in the quadrature amplitudes of the output beams. The existence of an Einstein-Podolsky-Rosen paradox is demonstrated through violations of the inferred Heisenberg uncertainty principle at causally unrelated locations in the output field. This provides a way of maintaining the commutation relations of the measured operators in the exact form envisaged originally by Einstein, Podolsky, and Rosen.

Correlations in nondegenerate parametric oscillation: Squeezing in the presence of phase diffusion.

We present a quantum theory of the nondegenerate parametric oscillator above threshold. The effect of signal and idler phase diffusion on the various types of external squeezing spectral measurements is discussed.

Theory of two-photon interference

The interference effects that can be observed in the two output arms of a lossless beam splitter are calculated for incident light in the form of a photon-pair excitation in the two input arms. The output state that occurs when the photon pair is excited in a single input arm resembles that expected for independent classical particles, whereas quantum interference effects occur when the photon pair is divided between the two input arms. Detailed output photocount correlation functions are calculated for two-photon input states produced by a two-atom light source, a degenerate or nondegenerate parametric oscillator in a high-Q cavity, and an atomic cascade emission light source.

Quantum analysis of intensity fluctuations in the nondegenerate parametric oscillator.

A quantum analysis of the intensity fluctuations is given for the nondegenerate parametric oscillator both above and below threshold. Theoretical analysis and experiments by Heidmann, Horowicz, Reynaud, Giacobino, and Fabre [Phys. Rev. Lett. 59, 2555 (1987)] have shown that a noise suppression below the vacuum level is possible in the difference of the intensities of the signal and idler modes. The effect of nonequal cavity decay rates and intracavity losses is shown to modify significantly the fluctuation spectra for the difference in the intensity of the signal and idler beams. The results of exact nonlinear solutions for the internal cavity modes are discussed. We demonstrate that a very sensitive absorption detector may be made by operating the oscillator near threshold.

Phase Cross-correlation in the Parametric Amplifier

Abstract Using the quantum theory of a non-degenerate parametric amplifier, we discuss the phase correlations between signal and idler modes well above threshold. Particular attention is paid to the influence which fluctuation of the driving laser has on these correlations. We point out that the signal and idler mode phase correlation may be tuned by control of the driving laser field intensity and linewidth. For coherent driving, the mode phases are negatively cross-correlated. We stress the qualitative importance of these mode correlations for a class of two-photon resonant excitation experiments in atoms. In particular, the non-degenerate parametric oscillator represents a concrete model of a source with negatively cross-correlated phase fluctuations.

Quantum correlations of phase in nondegenerate parametric oscillation.

The squeezing spectrum for nondegenerate parametric oscillation above threshold is calculated, including phase diffusion. A nonclassical correlation in phase and intensity occurs which is an example of the Einstein-Podolsky-Rosen paradox, even in fields of large photon number.

Generation of nonclassical photon states using correlated photon pairs and linear feedforward.

It is shown that nonclassical photon states can be produced by generating correlated photon pairs, measuring the idler mode, and manipulating the signal mode using feedforward and linear attenuators, amplifiers, or phase modulators. The minimum achievable Fano factor for such schemes is (2/\ensuremath{\pi}〈n〉${)}^{1/2}$, where 〈n〉 is the mean output photon number. A nondegenerate parametric oscillator followed by linear manipulators can reach this limit. A nondegenerate parametric amplifier followed by linear phase manipulation can produce phase-squeezed states. The minimum achievable phase noise is a factor 1/2G below that of a coherent state, where G is the amplifier gain. The advantages with these schemes are wavelength tunability, potentially very high squeezing bandwidth, and relative simplicity.

Phase correlation in nondegenerate parametric oscillators and amplifiers: Theory and applications.

The phase-fluctuation correlation between the signal and idler fields in nondegenerate parametric optical amplifiers and oscillators is analyzed. It is shown that close to the threshold pump power, the correlation is sufficient to reduce the phase fluctuations below those of a coherent state. The phase-fluctuation correlation is negative due to the simultaneous phase matching and energy conservation. This restricts the usefulness of the correlation. The pump source's phase noise will furthermore set a limit to the minimum achievable phase spectral density. The conditions for surpassing the standard quantum limit are elaborated. Finally, applications to coherent optical communication and gravitational wave detection are discussed.

Generation and amplification of number states by nondegenerate parametric oscillators with idler-measurement feedback.

Noise spectra of the in-phase and quadrature-phase components of the signal and idler fields of a nondegenerate optical parametric amplifier are calculated. It is shown that, as is suggested by the operator Manley-Rowe relations, the external in-phase (amplitude) fluctuations of the signal and idler fields are correlated in the frequency region lower than the signal and idler cavity bandwidths. If the idler photon flux is continuously measured and the photocurrent fluctuations are fed back to control the pump intensity, the signal output will feature an amplitude noise spectral density reduced to below the standard quantum limit (amplitude squeezing) in the frequency region below the feedback loop and signal and idler cavity bandwidths. An all-optical realization of such a negative-feedback parametric oscillator is presented. It is also shown that a nondegenerate parametric amplifier with idler measurement feedback can add a fixed number of photons to a photon-number state.