Probe Gain Research Articles

Control of the inversionless gain and refractive index in a V-type atom via squeezed vacuum and quantum interference

In this paper we analyze the steady-state populations and gain lineshape of a V-type three-level atom with a closely spaced excited doublet. The atom is driven by a strong coherent field, a weak probe, and a single broadband squeezed vacuum. We focus our attention in the interplay between the quantum interference and the squeezed field on the probe gain. It is shown that the relative phases between the two coherent fields and the squeezed field play an important role in the optical properties of the atom. Specifically, we find that the probe can experience gain without population inversion for proper values of the parameters characterizing the squeezed field and in the absence of incoherent pumping. The system can be tailored to exhibit multiple dispersion regimes accompanied by negligible gain or absorption over a large bandwidth, a desirable feature for obtaining propagation of pulses with negligible distortion.

Switching from positive to negative dispersion in transparent degenerate and near-degenerate systems

We investigate realistic atomic systems whose dispersion at line center switches from positive to negative and vice versa, as a particular experimental parameter is changed. We concentrate on those systems which have low probe absorption or gain at line center leading to a high figure of merit, and simultaneously have low pump absorption. For this purpose, we study both open and artificially closed ${F}_{g}=\stackrel{\ensuremath{\rightarrow}}{1}{F}_{e}=1$ and ${F}_{g}=\stackrel{\ensuremath{\rightarrow}}{1}{F}_{e}=2$ transitions in ${}^{87}\mathrm{Rb},$ in the absence and presence of an applied magnetic field. We find that the preferred system for observing switchover in the sign of the dispersion from positive to negative, as the pump Rabi frequency increases, is the open near-degenerate ${F}_{g}=\stackrel{\ensuremath{\rightarrow}}{1}{F}_{e}=1$ system. In the presence of Doppler broadening, the dispersion is positive for all realistic experimental parameters. Thus the switchover in the sign of the dispersion is only observable in the absence of Doppler broadening.

Probe gain with population inversion in a four-level atomic system with vacuum-induced coherence.

For a four-level atomic system with a doublet of closely spaced levels, we find that, owing to the coherence that results from the vacuum of the radiation field, population trapping at excited levels and probe gain with population inversion can be achieved with weak incoherent pumping. This gain is different from both the conventional lasing gain and gain without inversion in that there exists population inversion on probe transitions but the inversion is achieved by the vacuum-induced coherence.

Phase and amplitude control of the inversionless gain in a microwave-driven ?-type atomic system

In order to achieve the phase-sensitive probe gain without population inversion, we investigate a three-level Λ-type atomic system driven by a coherent field and a microwave field. It is shown that, by modulating the relative phase of applied fields, we can obtain quite high inversionless gain at different probe detunings and change the gain behavior of the probe correspondingly. We find that amplitudes of the coherent field and the microwave field are also important factors that can result in different gain behavior of the probe. Here, we use the microwave field to induce the quantum coherence between the two ground levels, which is necessary for phase-sensitive effects, since it can result in the interference between two different transition channels.

The probe gain with and without inversion in a four-level atomic model: light amplification at a short wavelength

We propose a new four-level atomic model for achieving light amplification at a short wavelength, where direct incoherent pumping into the top level is avoided by the advantage of coherent pumping. In this model, the lower level of the probe transition is an excited state but not the usual ground state. By analytical as well as numerical calculations, we find that the probe gain, either with or without population inversion, which depends on the relation between spontaneous decay rates γ42 and γ21, can be achieved with proper parameters. We note that the Raman scattering gain always plays an important role in achieving the probe amplification.

Phase control of the probe gain without population inversion in a four-level V model

We propose a new scheme for achieving inversionless gain that depends on both an internal interference effect and external coherent fields. We have found that, owing to the quantum interference effect that originates from spontaneous emissions from two closely lying levels, large inversionless gains can be achieved under appropriate conditions. In particular, in addition to the amplitudes, the phases of the applied fields also affect inversionless gain remarkably. That is to say, we can use the relative phase between two intense fields to control probe gain without inversion.

Response of the probe gain with or without inversion to the relative phase of two coherent fields in a three-level V model

We investigate a V-type three-level atomic system with two near-degenerate excited levels, which is driven by a strong coherent field and a weak probe field. We find that, due to the quantum interference between two spontaneous decay channels, even in the absence of an incoherent pumping, the probe gain can be achieved and modulated at different probe detunings just by tuning the relative phase between the probe and the coherent field to different regions. By demonstrating the gain-absorption coefficient as well as the population difference on the probe transition, we show that the probe gain can be either with or without population inversion, which depends on detunings, spontaneous decay rates, and the relative phase. In this atomic system, the phase-dependent probe gain originates from the internal quantum interference effect as well as the external dynamically induced coherence effect.

Phase dependence of the probe gain based on dynamically induced population inversion in a Λ system

Due to interaction with the vacuum of the radiation field, near-degenerate lower levels in a Λ system have an additional coherence term, the spontaneously generated coherence (SGC) term. For a Λ system without incoherent pumping, we discuss the dependence of both the dynamically induced population inversion and the probe gain on the relative phase of two coherent fields in the presence of SGC. We find that, the probe gain based on dynamically induced inversion can be achieved with proper relative phases. We support our results by numerical calculation and analytical explanation.

Resonant and off-resonant transients in electromagnetically induced transparency: Turn-on and turn-off dynamics

This paper presents a wide-ranging theoretical and experimental study of non-adiabatic transient phenomena in a $\Lambda $ EIT system when a strong coupling field is rapidly switched on or off. The theoretical treatment uses a Laplace transform approach to solve the time-dependent density matrix equation. The experiments are carried out in a Rb$^{87}$ MOT. The results show transient probe gain in parameter regions not previously studied, and provide insight into the transition dynamics between bare and dressed states.

Observation of transient gain without population inversion in a laser-cooled rubidiumΛsystem

We have observed clear Rabi oscillations of a weak probe in a strongly driven three-level lambda system in laser-cooled rubidium for the first time. When the coupling field is non-adiabatically switched on using a Pockels cell, transient probe gain without population inversion is obtained in the presence of uncoupled absorptions. Our results are supported by three-state computations.

Theory of a collective atomic recoil laser

We perform a study of a collective atomic recoil laser ~CARL! that goes beyond the initial growth period. The study is based on a theory that treats both internal and external degrees of atomic freedom quantum mechanically but regards the laser light as a classical field obeying Maxwell’s equations. We introduce the concepts of momentum families and diffraction groups and organize the matter wave equations in terms of diffraction groups. The steady-state lasing conditions are discussed in connection with the probe gain in the recoil-induced resonances. The nontrivial steady states and the linear stability analysis of the steady states are both carried out by the method of two-dimensional continued fractions. Both stable and unstable nontrivial steady states are calculated and discussed in the context of regarding the CARL as multiwave mixing involving many modes of matter waves and two optical fields.

Interference-induced gain in the Autler-Townes doublet of a V-type atom in a cavity

We study the Autler-Townes spectrum of a V-type atom coupled to a single-mode, frequency-tunable cavity field at finite termperature, with a pre-selected polarization in the bad cavity limit, and show that, when the mean number of thermal photons $N\gg 1$ and the excited sublevel splitting is very large (the same order as the cavity linewidth), the probe gain may occur at either sideband of the doublet, depending on the cavity frequency, due to the cavity-induced interference.

Cavity implementation of quantum interference in aΛ-type atom

A scheme for engineering quantum interference in a $\Lambda$-type atom coupled to a frequency-tunable, single-mode cavity field with a pre-selected polarization at finite temperature is proposed. Interference-assisted population trapping, population inversions and probe gain at one sideband of the Autler-Townes spectrum are predicted for certain cavity resonant frequencies.

Population inversion and probe gain in Autler–Townes doublet of a V-type three-level atom in a cavity

A cavity-modified master equation is derived for a coherently driven V-type three-level atom coupled to a single-mode cavity in the bad cavity limit. The influences of the cavity-induced quantum interference on the steady-state populations are analyzed. We show that population inversion can occur in atomic bare state representation. The probe absorption spectrum is also investigated. Various line shapes and probe gain with and without population inversion can appear in the Autler–Townes doublet due to the effects of the cavity-induced quantum interference.

Absorption Spectrum of a Driven Two-Level Atom in a Tunable Cavity with Injected Squeezed Vacuum

The absorption spectrum of a driven two-level atom in a frequency tunable cavity with injected squeezed vacuum is investigated. The line shape of the spectra depends on the relative phase between the driving field and the squeezed vacuum, and the frequency detuning between the driving field and the cavity mode. Line narrowing and probe gain can occur and be enhanced by adjusting the phase and detuning.

Propagation effects on lasing without population inversion

We study propagation effects on lasing without population inversion in a Doppler-broadened V-type three-level system. In particular, we focus our analysis on frequency up-conversion lasing without inversion in atomic rubidium. In an atomic beam configuration, we show that it is possible to increase notably the probe gain per single pass through the active medium by detuning driving and probe fields out of one-photon resonance but maintaining the two-photon resonance condition. In a vapour cell configuration, we show that due to propagation effects the probe gain per single pass depends strongly on the driving field intensity at the entrance of the active medium. In fact, for appropriate parameter values, it is possible to reach values of the probe gain per single pass of around 40%. For this last case, we have considered the feedback of a ring laser cavity.

Theory of pump-probe spectroscopy using an amplitude approach

A theory of pump probe spectroscopy is carried out using an amplitude approach in a bare state basis. The interplay between absorption and emission is clearly defined in this approach. Both closed and open systems are considered. The theory is applied to a calculation of the dispersion-like structure that appears when the probe frequency is nearly equal to the pump frequency, in the limit of large pump field detuning. The origin of the dispersion-like structure can be traced to interference terms in the absorption spectrum or to a radiative shift. The probe gain which occurs without level inversion cannot be viewed as a parametric process, in its normal sense.

Nonclassical gain in the optical Stark effect: density matrix approach

The optical Stark effect in a pump-probe setup is expected to show interesting additional features if the quantization of the pump field becomes important. A major effect is that the lineshape of a Stark-shifted resonance is strongly modified when squeezing the pump field. Furthermore, a probe gain is predicted here which does not appear in a semiclassical treatment. It appears for pump detunings considerably lower than the mean Rabi frequency. The nonclassical gain in the optical Stark effect is investigated on an ensemble of two-level systems (TLSs). A density matrix approach is presented which allows the accurate calculation of the probe absorption. The precise treatment of correlations between pairs of TLSs is crucial to explain details of the lineshape.

Comparison of recoil-induced resonances and the collective atomic recoil laser

The theories of recoil-induced resonances (RIR) [J. Guo, P. R. Berman, B. Dubetsky and G. Grynberg, Phys. Rev. A {\bf 46}, 1426 (1992)] and the collective atomic recoil laser (CARL) [ R. Bonifacio and L. De Salvo, Nucl. Instrum. Methods A {\bf 341}, 360 (1994)] are compared. Both theories can be used to derive expressions for the gain experienced by a probe field interacting with an ensemble of two-level atoms that are simultaneously driven by a pump field. It is shown that the RIR and CARL formalisms are equivalent. Differences between the RIR and CARL arise because the theories are typically applied for different ranges of the parameters appearing in the theory. The RIR limit considered in this paper is $qP_{0}/M\omega_{q}\gg 1$, while the CARL limit is $qP_{0}/M\omega_{q}\lesssim 1$, where $% q $ is the magnitude of the difference of the wave vectors of the pump and probe fields, $P_{0}$ is the width of the atomic momentum distribution and $% \omega_{q}$ is a recoil frequency. The probe gain for a probe-pump detuning equal to zero is analyzed in some detail, in order to understand how the gain arises in a system which, at first glance, might appear to have vanishing gain. Moreover, it is shown that the calculations, carried out in perturbation theory have a range of applicability beyond the recoil problem. Experimental possibilities for observing CARL are discussed.

Dynamics of a driven two-level atom coupled to a frequency-tunable cavity

A cavity-modified master equation is derived for a coherently driven two-level atom coupled to a single-mode cavity in the bad cavity limit, in which the cavity frequency is tuned to either the center or one of the sidebands of the Mollow triplet. The atomic populations in both the bare- and dressed-state representations are analyzed in terms of the cavity-modified transition rates. In the bare-state basis, the role of the cavity may be interpreted as enhancing the stimulated absorption of the atom while suppressing the stimulated emission. The bare-state population may thus be inverted under appropriate conditions. The dressed-state inversion, however, originates from the enhancement of the atom-cavity interaction when the cavity is resonant with the atomic dressed-state transition. We show that two-phase quadratures of the atomic polarization decay at different rates. The decay of the in-phase (or out-of-phase) quadrature may be greatly inhibited as the driving intensity increases, depending on the cavity resonant frequency. The spectrum of the atomic fluorescence emitted out the side of the cavity is also studied. The spectral profiles are sensitive to the cavity frequency. When the cavity frequency is tuned to the center of the Mollow resonances, the fluorescence spectrum is symmetrical with three peaks whose linewidths and heights are intensity dependent. When the cavity frequency is tuned to one of the Mollow sidebands, however, it is asymmetric, and the central peak and the sideband on resonance with the cavity can be significantly suppressed for strong driving fields. All three spectral lines can be narrowed by increasing the Rabi frequency. The physics of these striking spectral features is explored in the dressed-state basis. We also investigate the probe absorption spectrum. When the cavity frequency is tuned to the center of the Mollow fluorescence triplet, the central component exhibits a Lorentzian line shape, while the side bands show the Rayleigh-wing line shape. Probe gain may occur at line center due to cavity-induced, bare-state population inversion. When the cavity is tuned to resonance with one sideband, only two sidebands, with Lorentzian profiles, dominate. Gain can occur at the sideband far off resonant with the cavity. The sideband gain is a consequence of an unbalanced dressed-state population distribution.