Two-photon Coherence Research Articles

Squeezed cascade lasers without and with inversion

A cascade system can produce lasers with and without inversion simultaneously. Lasing without inversion is maintained by two-photon coherence. Here we examine the quantum statistical properties of cascade lasers from a four level atomic system with two incoherent steps. It is shown that cascade lasers with and without inversion may simultaneously exhibit sub-Poissonian statistics. The intensity fluctuation spectrum in each laser field is reduced up to 25% below the shot noise limit. The succession of the two incoherent steps is responsible for noise reduction. At the same time, we investigate the fluctuation spectrum in the output intensity difference. For a broad range of parameters, up to 50% squeezing is achieved. The physical mechanism is attributed to the ac-Stark effect. In particular, when the present four-level system is reduced to the three-level system, up to 50% squeezing is retained.

Demonstration of a phase conjugate resonator using degenerate four-wave mixing via coherent population trapping in rubidium

We demonstrate a ring cavity laser using the gain mechanism of a four-wave mixing process, mediated by two-photon Zeeman coherence resulting from coherent population trapping in a rubidium vapor cell. The cell acts as an amplifying phase conjugate mirror at one corner of the ring cavity. Even though the fundamental process requires non-degeneracy between the probe and the conjugate in the atom's frame, they are degenerate in the laboratory frame, via selection of a moving band of atoms for the gratings. As such, no frequency shifting is necessary in the cavity. The polarization orthogonality of the probe and the conjugate is compensated by an intra-cavity quarter wave plate.

Effect of interference between three-level inversions on the inversion process and amount of inversion in a four-level system

In a four-level -system interacting with three coherent laser pulses, interference between population inversions in coupled three-level ladders is examined. The interference effect, which affects the process and the completeness of the inversion, is represented by the two-photon coherence. It is shown that, in the adiabatic passage method, the phase and the scaling factor of the two-photon coherence are zero and a constant, respectively, resulting in no interference effect, but, in the optimal detuning method, they are strongly time dependent enough to represent the interference effect to change the process and the amount of inversion significantly. In the latter method, the ratio of Rabi frequencies for the four-level inversion to be completed, which is changed by the interference effect, is obtained.

Geometrical representation of coherent-excitation methods using delayed and detuned lasers

A precessing vector model has been developed for the geometrical interpretation of the adiabatic following and the optimal detuning methods, which play a decisive role in coherent population transfer in a three-level system. In our model, the Bloch vector defined by a population inversion and two-photon coherence components precesses about the torque vector consisting of an effective Rabi frequency and detuning components. The Bloch vector traces out different routes depending on combinations of the time delay of two laser pulses and detunings from the resonant frequencies. For the extreme cases where the optimal detuning with zero delay and the optimal delay with zero detunings are taken, our vector model with analytical solutions is compared with numerical solutions.

Observation of the ultrafast two-photon coherent biexciton oscillation in a GaAs/AlxGa1-xAs multiple quantum well.

Polarization-dependent heterodyne four-wave-mixing measurements with a phase-conjugate Michelson interferometer reveal a macroscopic nonradiative 770-THz oscillation in the nonlinear optical susceptibility of GaAs multiple quantum wells. The oscillation is interpreted as the temporal evolution of the two-photon nonradiative biexcitonic coherence.

Generation of squeezed light via spontaneous emission from a three-level cascade system

A theoretical investigation is made into the possibility of generating squeezed states of light in spontaneous emission from a three-level atom. Spontaneous emission is known as a source of the noise which destroys coherence effects. We find that rather than destroy squeezing, spontaneous emission from a three-level cascade system can actually create squeezing in an initially unsqueezed source field provided the atom is initially prepared in a suitable superposition of its states. We show that the ability of a three-level atom to generate squeezing of the source field via spontaneous emission relies on the presence of non-zero two-photon coherences that are not present in two-level atoms, in which source field squeezing only occurs if it is present initially.

Lasing without inversion in the absence of a coherent coupling field.

We analyze the inversionless gain in a three-level ladder system by replacing the usual coherent coupling field with an incoherent field. Surprisingly, it is found that one can obtain inversionless amplification of a weak probe even in the absence of a coherent field in the model. We conclude that gain is determined by the ensemble average of the product of the two-photon coherence and the ``effective Rabi frequency'' of the field. Thus, even though the incoherent pump reduces the two-photon coherence, gain can be restored by choosing sufficiently high strengths of the incoherent field.

Polarization dependent four-wave-mixing and two-photon coherence in solids

Polarization dependent degenerate-four-wave-mixing experiments on semiconductors (ZnSe, CdS) and dielectrics (NaCl, PbF/sub 2/) reveal the essential mechanisms of the bound-electronic /spl chi//sup (3)/. We show, for the first time, that the observed anomalous dispersion of the polarization dependent phase-conjugate reflectivity can be explained using a simple 3-band model. The near vanishing reflectivity in the two-photon coherence geometry is shown to be a consequence of the interference between transitions originating from heavyand light-hole valence bands. We also present measurements on the polarization dichroism of the nonlinear refractive index (n/sub 2/), in good agreement with this simple theory. >

Probing the two-photon phase coherence of parametrically down-converted photons by a local oscillator.

A degenerate beam of down-converted photon pairs from a nonlinear crystal pumped by pulsed light was mixed with coherent local oscillator pulses by a beam splitter, and the coincidence rate for detections of photons at the two output beams was measured. The coincidence rate showed interference fringes as the phase difference between the pump light and the local oscillator was varied. It showed a negative correlation in some range of the phase difference.

Polarization-dependent coherent nonlinear optical response in GaAs quantum wells: Dominant effects of two-photon coherence between ground and biexciton states

Using the unique polarization selection rule for the biexcitonic transition we demonstrate conclusively the dominant effects of the biexciton-induced two-photon coherence on polarization-dependent four-wave-mixing in GaAs quantum wells. We also show that the two-photon coherence is the leading contribution to the self-diffracted four-wave-mixing response in the cross-linearly polarized configuration and can explain the anomalous polarization dependence in four-wave-mixing.

Steady-state squeezing in a driven three-level Lambda system.

The occurrence of steady-state squeezing in a coherently driven three-level atom of the configuration is found to be highly sensitive to the detection process of the fluorescence field. We show that there is no steady-state squeezing when the two atomic transitions equally contribute to the detected fluorescence field. There is no squeezing even when only one of the two possible transitions contributes to the detected fluorescence field, if the decay rate of the contributing transition is smaller than or equal to the decay rate of the other transition. Squeezing may occur only when the decay rate of the transition that exclusively contributes to the detected fluorescence field is larger than the decay rate of the other transition. Moreover, when the squeezing attains its maximum value, pure two-level squeezing is involved. The system reduces to a two-level system in which both the basic three-level dynamics and the two-photon coherences are destroyed.

Optimum field squeezing from atomic sources: Three-level atoms.

Light emitted from laser-driven atoms often has squeezed quadrature fluctuations reflecting the phase dependence of the atomic source excited into a coherent superposition by the driving field. In this paper, we study the maximum squeezing in the emitted light fields from three-level atoms, paying particular attention to the role of atomic coherences in governing the optimum squeezing which is possible. Some phase dependent nonlinear optical processes have the potential for substantial quantum noise reduction at useful intensities: for example, four-wave mixing involving atomic systems has already been used to generate quadrature-squeezed light. The threoretical description of such a source is generally complicated with damping processes, coherent and incoherent pumping, and so on, all needing to be taken into account. Fully quantum treatments are available, but the basic physics of the process is often difficult to grasp in the necessarily complicated analysis. Although less important from the point of view of efficient practical sources of squeezed light, studying the generation of squeezed light in simpler systems such as two- or three-level atoms interacting with one or two modes (as in Jaynes-Cummings models) or in spontaneous emission or resonance fluorescence gives greater insight into the fundamentals of the squeezing process. In particular, the relationship between the atomic coherences and the degree of squeezing in the generated fields can be explored. We study the maximum (optimized) squeezing that can be obtained in the emitted fields from the irreversible decay from three-level atoms for any choice of initial conditions, excitations and decay process, for all quadrature components and for all possible configurations (V, , and ladder systems). We show that for V and systems, optimum squeezing is actually associated with a two-level state (in a suitable basis) involving a single one-photon coherence, but for ladder systems the state for maximum noise reduction is not equivalent to a two-level system and involves a single two-photon coherence and no intermediate state population. We pay particular attention to whether the total field is in a minimum uncertainty state, and the nature of the atomic state associated with maximum squeezing, especially whether it is a mixed or pure state. In the case where the initial free field has a zero amplitude at the detector and the source atoms are confined to a region small compared to the wavelength (Dicke source) we show that the squeezing in the total field is given in terms of the squeezing in the source field, and hence related to atomic populations and atomic one-photon and two-photon coherences for the case of three level atom. Previously unconsidered source-free field interferences terms are shown to be zero. The choice of quadrature phase and frequency is optimized to minimize the source field normally ordered variance. We then minimize further with respect to the choice of atomic density matrix elements subject to the constraints that the density matrix is Hermitean, positive, and has a trace equal to unity. In all cases we find that the optimum squeezing is produced when the source field is in a minimum uncertainty state.

Transparency Induced by Two-Photon Coherence in the V-Shaped Three-Level System

We have investigated the steady-state behavior of a V-shape three-level system submitted to the radiative field and to the relaxation process. The coherence induced by simultaneous two-photon transition leads to a strong decrease of medium absorption. In this case, the peak of transparent spectrum is 7 times higher than that of saturant spectrum.

Squeezing from ghost transitions.

We show that significant squeezing in a strong signal light field can be generated with three-level atoms in a ghost-transition setup by tuning a weak probe beam inside the Autler-Townes doublet created by the strong signal light. Close to the Rabi level, i.e., within the absorption line, processes involving both amplitude quadratures become important. Significant atomic two-photon coherence provides a vehicle for signal-amplitude fluctuations to trigger fluctuations in the probe amplitude. Subsequently, atomic coherence will feed these probe fluctuations back into the signal and enable substantial noise suppression.

Squeezing in two-atom resonance fluorescence induced by two-photon coherences

We examine squeezing properties of resonance fluorescence from two interacting atoms. Previous theoretical analyses of this model have predicted squeezing on one-photon resonance. Here we show that it is possible to obtain squeezing in two-atom resonance fluorescence through two-photon transitions induced by a cooperative atomic interaction. The squeezing occurs near a two-photon resonance and is not sensitive to the duration of the detection time in comparison with the decay time of the subradiant state. Moreover, squeezing near a two-photon resonance is completely independent of the direction of observation in respect to the atomic axis and can be significantly larger than that previously found on one-photon resonance.

Photon echo induced by two-exciton coherence in a GaAs quantum well.

Excitonic nonlinearities in the weak-excitation limit condition are examined with time-integrated and time-resolved four-wave mixing (FWM). Below an excitation of 3\ifmmode\times\else\texttimes\fi{}${10}^{9}$ excitons/${\mathrm{cm}}^{2}$, coherent third-order processes prevail. Echo-type signals are observed in parallel and perpendicular polarization configurations. The coherent process induced by the two-photon coherence of the two-exciton state is attributable to signals in the perpendicular configuration. The polarization dependences of a temporal profile and the intensity of FWM signals are well explained with third-order perturbational analysis that takes into account the two-exciton states and inhomogeneity.

Gain in a three-level Lambda system driven by a single pump.

We calculate the absorption spectrum of a weak probe interacting with a \ensuremath{\Lambda}-shaped three-level system driven by a single pump. We find that there are four types of terms that contribute to the probe absorption: population-difference and two-photon coherence terms which derive solely from interaction with the pump (dc terms) and population-difference and two-photon coherence terms that pulsate at the pump-probe frequency offset. We find that the main features of the probe spectrum derive from the pulsating terms whereas the dc terms either interfere destructively with each other or with the pulsating terms. This is a clear extension to the three-level system of the concept of light amplification by coherence. We calculate the spectrum for three cases: (i) a degenerate population-trapped system, (ii) a degenerate system in which both transitions are population inverted, and (iii) a nondegenerate population-trapped system. The results of case (i) are similar to those for the two-level system but the population-trapped system has the advantage of avoiding pump absorption. We show that the Rabi frequency of the nonabsorbed pump can be found by determining the probe frequencies at which probe nonabsorption occurs. In (ii), the results are compared with the case where two pumps interact resonantly with a nondegenerate system. In (iii), we find that the populations in the lower states behave dispersively as a function of the pump detuning. For Rabi frequencies that are small compared to the separation between the lower levels, the lower level nearer to resonance is less populated than the other level. However, at higher Rabi frequencies, the situation is reversed. The probe spectrum contains two absorption peaks when the pump Rabi frequency is small and two emission peaks when it is large.

Two-photon Coherence and Steady-state Saturated and Inverted Populations in Three-level Systems

Abstract We study the correlation between level populations, absorption and two-photon coherence in closed Λ- and V-shaped three-level systems interacting with two lasers of arbitrary intensity. Whereas it is well known that maximum two-photon coherence leads to population trapping in Λ-shaped three-level systems interacting with two equally detuned lasers, we demonstrate that minimum two-photon coherence, under saturation conditions, can lead to equal populations in all the levels of a Λ- or V-shaped system when the lasers are symmetrically detuned. Moreover we show that steady-state population inversion between one of the upper levels of a V-shaped system and the ground state can occur when either the detunings are asymmetrical or the upper states decay at different rates. It is shown that this population inversion does not lead to stimulated emission into the lasing modes. These effects are also correlated with two-photon coherence and are explained physically by a cross three-photon scattering process...

Probing the phase coherence of parametrically generated photon pairs: A new test of Bell's inequalities

We show that the two-photon phase coherence of parametrically generated photon pairs, which is at the origin of squeezed-light generation, can be directly probed using an intensity-correlation measurement. The resulting intensity correlation leads to a new violation of Bell's inequalities, which could be experimentally tested.

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.