Quantum Theory Of Multiwave Mixing Research Articles

双模输出纠缠激光的非局域性与非经典性研究

Output nonlocality and nonclassicality for the two modes are investigated in an entanglement laser system. Within the framework of a quantum theory of multiwave mixing, nonlocality and nonclassicality are discussed according to the violations of Bell inequality and Cauchy-Schwarz inequality. It is found that both nonlocality and nonclassicality can be fulfilled in the outside cavity fields under certain conditions. It is also shown that there are some nonclassical states that do not show nonlocality.

VIOLATION OF CLASSICAL INEQUALITIES AND EPR CORRELATIONS IN A TWO-MODE THREE-LEVEL ATOMIC SYSTEM

We investigate violation of Cauchy–Schwarz and Bell inequalities in two-mode three-level cascade system with injected atomic coherence in the framework of quantum theory of multiwave mixing. We show that Cauchy–Schwarz inequality is strongly violated when there is strong entanglement in the system. It also appears that Bell inequality is violated in the region where there is weak entanglement and well-preserved where there is strong entanglement in the system. We thus note that there are states which are entangled but do not violate Bell inequality. We also show that this system can be used to prepare states that exhibit EPR correlations.

Continuous Variable Entanglement and Violation of BellInequality for Two Modes in a Three-Level Cascade Atomic System

Continuous variable entanglement and violation of Bell inequality fortwo modes are investigated in a three-level cascade atomic system.Entanglement of the system is demonstrated according to the entanglementcriterion [Phys. Rev. Lett. 84 (2000) 2722]. Violation of Bellinequality is studied within the framework of a quantum theory ofmultiwave mixing. It is shown that there are some states that areentangled but do not violate the Bell inequality.

Quantum theory of multiwave mixing with a local field correction

In this paper, we calculate the four coefficients for the quantum theory of multiwave mixing including a local-field correction resulting from dipole-dipole interactions. We make contact with the semiclassical calculations of probe absorption and four-wave-mixing coupling coefficients, and illustrate the effects of local field corrections on resonance-fluorescence and coupled-mode-fluorescence spectra. The method uses the hybrid quantum-Langevin-equation master-equation approach of An and Sargent.

Enhanced squeezing in a squeezed vacuum

A quantum theory of multiwave mixing based on a combination of a Langevin quantum regression method and a density operator technique is outlined. The approach is simple, yet general, and is particularly valuable for analyzing complicated media such as semiconductors. We apply it to find the quantum multiwave mixing equations in a squeezed vacuum. Comparing squeezing spectra in squeezed and ordinary vacua, we find significantly enhanced squeezing for the appropriate pump-vacuum relative phase.

Quantum theory of multiwave mixing: Squeezed-vacuum model.

The present paper combines a Langevin quantum-regression method with a density-operator approach to derive the master equation for the quantum theory of multiwave mixing in a very efficient way. The approach is quite general and is particularly valuable for analyzing complicated media such as semiconductors. It is used in the present paper to derive the quantum multiwave-mixing equations in a squeezed vacuum. We find improved formulas for resonance fluorescence in a squeezed vacuum as well as the squeezing coefficients in a squeezed vacuum. Comparing squeezing spectra in squeezed and ordinary vacua, we find significantly enhanced squeezing for the appropriate pump-vacuum relative phase.

Theory of a two-level quantum-beat laser.

The theory of a two-level quantum-beat laser is presented within the framework of the quantum theory of multiwave mixing. The diffusion coefficients for the relative and the mean of phase angles of the two modes are derived. It is shown that under suitable conditions the diffusion coefficient for the mean angle of the field modes vanishes.

Quantum theory of multiwave mixing. X. Two-photon three-level model.

We present a fully quantum-mechanical theory of nondegenerate multiwave mixing processes in three-level cascades with a two-photon pump. The explicit formulas for the resonance fluorescence spectrum and the quantum combination-tone source term are derived. The theory is applied to the generation of squeezed states of light. We find almost perfect squeezing for some strong-pump intensities and tunings within the Rabi sidebands. We find good broadband squeezing for low-pump intensities and tunings outside a small region around central tuning. Both cases avoid regions of significant spontaneous emission.

Violation of Cauchy-Schwarz and Bell's inequalities in four-wave mixing.

Certain nonclassical effects in four-wave mixing are studied within the framework of a quantum theory of multiwave mixing. It is shown that the Cauchy-Schwarz and Bell's inequalities are violated for large detuning of the pump frequency from the side-mode frequencies.

Quantum theory of multiwave mixing. IX. Squeezed states in two-photon media.

We apply our quantum theory of multiwave mixing for the two-photon two-level model to the generation of squeezed states of light. Because of the two-photon transition, a larger number of interaction potentials are present compared to one-photon models, leading to effects absent in the one-photon case. The two most significant of these are the appearance of dynamic Stark shifts and conjugate scattering off the pump induced two-photon coherence. We show that this can lead to almost perfect squeezing, even for low pump intensities and low detunings from the two-photon resonance.

Quantum theory of multiwave mixing. VIII. Squeezed states.

We apply our quantum theory of multiwave mixing to the generation of squeezed states of light via three- and four-wave mixing in cavities and in propagation. We compare the cavity predictions to the experimental results of Slusher et al. [Phys. Rev. Lett. 55, 2409 (1985)], finding reasonably good agreement. The squeezing found there is due to the fact that the number operators are driven by resonance fluorescence, which nearly vanishes for the large detunings chosen, while the combination tone operators are driven by relatively large source terms. We give a physical discussion as to why the spectral quantities outside the cavity are given by those inside multiplied by the cavity linewidth. We have found analytic formulas for the variances for arbitrary propagation distances, detunings, and pump intensities. We derive these formulas both from the density operator and from the Langevin methods. To obtain significant squeezing, the propagation distances must be large compared with the resonant Beer's law length.

Solution of the quantum coupled mode equations

From our quantum theory of multiwave mixing, we obtain coupled mode equations that treat the sideband fields quantum mechanically. This allows the inclusion of the effects of quantum noise on the sideband fields. We solve the quantum coupled mode equations for arbitrary atomic and pump/probe detunings, and illustrate our results for the generation of squeezed states of light using four-wave mixing.

Generation of squeezed states by nondegenerate multiwave mixing in two-level media

Using our quantum theory of multiwave mixing, we derive formulas for the intracavity squeezed variances generated by nondegenerate four-wave mixing in a cavity and illustrate the results with variance spectra as functions of side-mode/pump beat frequency.

Quantum theory of multiwave mixing. VII. Connection to quantum Langevin theory.

We transform our quantum theory of multiwave mixing, which is based on a reduced density operator, to the corresponding nondegenerate quantum-noise Langevin equations. We derive the diffusion coefficients from the drift coefficients using the generalized Einstein relation and illustrate the resulting quantum Langevin theory of multiwave mixing by specializing to the Reid and Walls degenerate theory of squeezed states of light.

Quantum theory of multiwave mixing. V. Two-photon two-level model.

We extend our theoretical formalism describing how one strong classical wave and one or two weak quantum-mechanical waves interact in a nonlinear medium to the ``two-photon two-level'' model. In this model, field transitions between two levels not connected by an electric dipole occur by means of a two-photon transition using off-resonant intermediate levels. This model has many similarities with, as well as significant differences from, the corresponding one-photon two-level model that has been treated in the previous papers in this series. The theory yields the first detailed calculation of the two-photon resonance fluorescence spectrum, as well as the complete set of four coefficients that describe the quantum theory of two-, three-, and four-wave mixing.

Quantum theory of multiwave mixing IV Effects of cavities on the spectrum of resonance fluorescence

In the presence of a high-finesse cavity, the resonance fluorescence spectrum can be altered by stimulated emission and multiwave mixing processes. We show that under some conditions it is possible for spontaneous emission to induce conjugate fields similar to semiclassical phase conjugation, requiring the use of the multiwave quantum theory described in earlier papers in this series. The theory is applicable to laser spectroscopy and optical bistability. We present explicit spectra and suggest possible experimental tests. In particular we find a quantum limit for FM spectroscopy that shows that even if the medium under study leaves the FM phase and amplitude relationships intact according to semiclassical theory, spontaneous emission can create an AM component detectable in a square-law detector.

Quantum theory of multiwave mixing. III. Averages over inhomogeneous broadening, spatial hole burning, and Gaussian beams.

The effects of inhomogeneous broadening, spatial hole burning, and Gaussian beams are calculated for the four coefficients derived in previous papers in this series [Phys. Rev. A 31, 3112 (1985); 31, 3124 (1985)] on the quantum theory of multiwave mixing. These coefficients uniformly describe how one or two strong classical-field modes and one or two weak quantum-field modes interact in a two-level medium. The phenomena for which this theory is applicable includes resonance fluorescence, Rayleigh scattering, laser and/or optical bistability instabilities, and phase conjugation. The averaged formulas are illustrated by resonance-fluorescence spectra. We find the sidepeaks can be ``washed out'' and that asymmetries can occur.

Quantum theory of multiwave mixing. II. Operator approach.

This paper treats the interaction of one strong classical field mode and one or two weak quantal modes with two-level systems. The analysis is carried out in a purely operator formalism that complements the method presented in the preceding paper and produces the same results. The present approach automatically collects all contributions to second order in the weak-field interactions, and can be easier to extend to more complicated cases. The analysis allows one to treat problems such as predicting the growth of sidemodes in laser- and optical-bistability instabilities, the resonance fluorescence spectrum, Rayleigh scattering, and quantum noise in small-signal phase conjugation.

Quantum theory of multiwave mixing. I. General formalism.

We present a theory that describes how one strong classical wave and one or two weak quantum-mechanical waves interact in a nonlinear two-level medium. The analysis is applicable to several popular problems with and without cavities. In particular, the theory treats laser and optical bistability instabilities, predicting when the instabilities grow from spontaneous emission. The theory is a multimode extension of Scully-Lamb theory that derives the equations that describe population pulsations, combination tones, mode locking, resonance fluorescence, Rayleigh scattering, and phase conjugation with quantum-mechanical fields. Hence the theory both presents new results on instabilities and phase conjugation, and also unifies the treatment of a variety of phenomena in the context of Lamb theory. The present paper (first of the series) presents the basic formalism, leaving most applications to subsequent papers in this series. The following paper presents equivalent derivations based on a purely operator formalism.