Nondegenerate Multiwave Mixing Research Articles

Quantum control and manipulation of multi-color light fields

Quantum control of stationary multi-color (MC) light fields in resonant medium with multi-Λ scheme of atomic transition is proposed. We have found the general analytical solution in the adiabatic limit of quantum evolution resulting from the interaction of the slow probe light with the new fields generated in the nondegenerate multi-wave mixing scheme. We have found a critical condition for the stopping and quantum manipulation of the MC-light fields where the united light group velocity can be reduced down to zero with optimal spectral parameters while preserving the delicate quantum correlations of the initial probe light pulse. The manipulations, which provide the effective transference of quantum probe light to the new multifrequency light fields have been analyzed.

Quantum theory of nondegenerate multiwave mixing: effect of pump phase fluctuations

We extend the quantum theory of nondegenerate four-wave mixing by including the effects of the finite bandwidth of the driving-pump field. The interaction of a beam of two-level atoms with the two opposite driving-pump fields that have finite bandwidth inside a bimodal cavity is considered. The master equation for the cavity-field modes, averaged over the stochastic process, is derived. We use our theory to study the effects of phase fluctuations, associated with the driving-pump field, on the generation of two-mode squeezing inside the cavity. The steady-state squeezing is achieved with the same driving-pump field as a local oscillator in the balanced homodyne-detection system. Our results show that, in spite of instantaneous phase locking between the cavity field and the local oscillator, the time-delay effects associated with the exponential decay of atomic coherence relate the steady-state squeezing to the diffusion constant of the driving-pump field.

Quantum theory of nondegenerate multiwave mixing. II. Adiabatic elimination via slowly varying amplitude approximation.

In this paper, we continue our development of the quantum theory of nondegenerate multiwave mixing in an atomic medium [Phys. Rev. A 37, 2017 (1988)]. In our development, the atomic variables are eliminated using a frequency-domain approach employing a slowly varying amplitude approximation that is more rigorous than the usual adiabatic approximation. We then specialize to the case of four-wave interaction with two strong pump beams and obtain noise correlations of the atomic polarization that are applicable to nondegenerate four-wave mixing. The noise correlations include the effect of atomic collisions that is crucial to the atomic-vapor experiments. After making the usual rotating-wave approximation, the atomic-polarization equations give us a set of temporal coupled-mode equations for the c-number variables corresponding to the annihilation operators. We then further specialize to the single-beam case in which all the relevant modes of interest are collinear and obtain a paired set of coupled-mode equations. In order to apply the theory to experiments employing traveling-wave interaction geometries, in the following paper of this series we will present a formalism to treat the spatial propagation of a quantum field.

Nondegenerate multiwave mixing in polydiacetylene: phase conjugation with frequency conversion

We present an analysis of optical phase conjugation with frequency doubling in terms of nondegenerate six-wave mixing fifth-order nonlinear susceptibility. We show how the Bragg phase-matching condition is achieved at small angles. The process under picosecond-pulse conditions in a polydiacetylene solution pumped at two-photon resonance and probed at one-photon resonance is experimentally demonstrated. Results are discussed in terms of a one-dimensional quantum three-level system. The proximity of one- and two-photon resonance in conjugated polymers makes these polymers efficient nonlinear-optical materials for this original application. The experiment permits artifact-free measurement of the two-photon state recovery time of the red form of polydiacetylene.

Quantum theory of nondegenerate multiwave mixing III Application to single-beam squeezed-state generation

We apply our quantum theory of nondegenerate multiwave mixing [ Phys. Rev. A37, 2017 ( 1988)] to squeezed-state generation experiments with two-level atoms. Our main interest is to predict the amount of squeezing achievable with a Doppler-broadened two-level medium. We are particularly interested in the single-beam configuration, in which all four interacting beams are spatially degenerate. We analytically solve the coupled-mode quantum Langevin equations for nondegenerate four-wave mixing. The solutions are used to compute the amount of squeezing. In the computation the effects of pump–probe phase mismatch, collisions, Doppler broadening, and Gaussian-intensity variation are comprehensively taken into account for the first time to our knowledge. Simple rules of thumb as to where one can see squeezing in both degenerate- and nondegenerate-frequency cases are derived by examining the limit of a short medium. We then present the case of an infinitely long medium, in which maximum squeezing is achieved when there is no pump–probe phase mismatch. With the inclusion of pump–probe phase mismatch, however, the maximum amount of squeezing is obtained with a finite-length medium instead. This prompts us to investigate in detail the finite-length medium case. Our results show that the effects of Doppler broadening and Gaussian-intensity variation can be largely circumvented by detuning the pump frequency more than three Doppler half-widths from resonance and that good broadband squeezing can be achieved even with a Doppler-broadened medium that has a moderate amount of collision broadening. Under these circumstances it is found that the effect of pump self-focusing or defocusing will be the major factor that limits the amount of achievable squeezing. In particular, the spatially varying nonlinear refractive indices seen by the pump and the probe modes are quite different, which causes the former to become spatially mismatched with the latter in the region in which strong squeezing is otherwise expected.

Theory of multiwave mixing in a squeezed vacuum

We present a theory of nondegenerate multiwave mixing in a squeezed vacuum. The probe absorption and coupling coefficients are derived using a standard Fourier-series method. We average the coefficients over pump spatial holes and solve the coupled mode equations to find the four-wave-mixing reflection coefficient. Reflectivity peaks and dips are found to be narrower than in an unsqueezed vacuum. Both the absorption and the reflectivity provide sensitive ways to measure the amount of squeezing in the vacuum.

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.

Quantum theory of nondegenerate multiwave mixing: General formulation.

In this first paper of a series on the quantum theory of nondegenerate multiwave mixing applicable to traveling-wave interaction geometries, we describe our problem formulation. We consider the explicit dynamics of a subset of the field quantization modes interacting with a system of stationary two-level atoms contained in a volume much smaller than the field quantization volume. Because we make the realistic assumption of leaving the remaining infinite set of field modes as a common thermal-field reservoir, the resulting Langevin equations contain extra decay terms due to collective spontaneous emission or super-radiance. We show that all but one of these super-radiance terms are negligible in the following two limits: (a) when the number of atoms in a diffraction volume is small; (b) when the atoms are pumped far off resonance. There is, however, an anomalous decay term which does not appear in a classical model of super-radiance based upon coherently phased atomic dipoles. The magnitude of this anomalous term is neither dependent upon the number of atoms nor on the pump-frequency detuning and may not be negligible at a low pump intensity. Neglecting the super-radiance terms, we then present a general Fourier-expansion solution technique for obtaining the atomic polarization in the presence of any number of field modes. The expansion is shown to be convergent in a commonly occurring situation in which all the strong pump modes are frequency degenerate and the remaining nondegenerate modes are all weak compared to the atomic saturation intensity. In subsequent papers of this series, we will present methods to treat, with some rigor, the spatial propagation of an interacting multimode quantum field and apply these methods to traveling-wave squeezed-state generation experiments.

Quantum theory of nondegenerate multiwave mixing.

Quantum theory of nondegenerate multiwave 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.

Optical phase conjugation with frequency up-conversion via high-order, nondegenerate multiwave mixing

One proposes a new way of getting optical phase conjugation, associated to frequency conversion (namely, frequency doubling, frequency multiplication or mixing), within a broad angular field of view. This technique is based on nondegenerate, higher order multiwave mixing in a phase-matched backward configuration. Applications to wave front reversal, spatial or temporal information processing with frequency up-conversion are outlined.