Observations of a doubly driven V system probed to a fourth level in an N configuration are reported. A dressed-state analysis is also presented. The expected three-peak spectrum is explored in a cold rubidium sample in a magneto-optic trap. Good agreement is found between the dressed-state theory and the experimental spectra once light shifts and uncoupled absorptions in the rubidium system are taken into account.

Observation of transient effects in electromagnetically induced transparency ͑EIT͒ is reported in Rb 85 cooled in a magneto-optical trap. The transmission of a weak probe beam in resonance with the 5S 1/2 (Fϭ3) to 5P 3/2 (Fϭ3) hyperfine transition increased transiently when a relatively strong coupling field in resonance with the 5S 1/2 (Fϭ2) to 5 P 3/2 (Fϭ3) hyperfine transition was switched on rapidly using a Pockels cell. The probe transient showed an initial Rabi half-cycle overshoot before settling down to steady-state EIT. The results agreed well with computations using a three-state model of the ⌳ system. The computations also suggest that transient gain should be observed with coupling field power only four times larger than that presently available to us. ͓S1050-2947͑98͒03308-3͔PACS number͑s͒: 42.50. Gy, 32.80.Pj, 42.50.Md The steady-state absorption of a weak resonant probe beam can be reduced or even eliminated by the presence of a strong coherent coupling beam exciting a linked transition. This effect, known as electromagnetically induced transparency ͑EIT͒, was first observed in 1991 ͓1,2͔. Related work on coherent population trapping in three-level systems dates from the mid-1970s and has been recently reviewed ͓3͔. In the last few years steady-state EIT has been widely studied in vapor cells and more recently in laser-cooled samples, see reviews ͓4,5͔. Transient EIT effects, however, have received relatively little explicit attention. In the first EIT experiments ͓1,2͔ the coupling field was provided by a high power pulsed laser with pulse rise and fall times that were slow compared with the Rabi period of the field. The transient approach to transparency in this adiabatic regime has been analyzed by Harris and Luo ͓6͔ from the point of view of energy requirements for the establishment of the transparency. We are interested in the nonadiabatic regime where the coupling field is switched on in a time that is short compared with Rabi periods and relaxation times. The only reported experimental study in this regime is that of Fry et al. ͓7͔, who observed transient absorption of a probe pulse in a ⌳ system immediately after the coupling beam was rapidly switched off. This is the converse of our experiment where the coupling field is rapidly switched on. Three-state models of transient effects in probe transmission when the coupling field is switched on nonadiabatically have been reported ͓8,9͔. In these models the transmission of a weak resonant probe approaches the steady-state EIT via damped oscillations characterized by the Rabi frequency of the relatively strong coupling field ⍀ C and the excited state decay rate ⌫, and for a sufficiently strong coupling beam there are intervals of probe gain without inversion, even without incoherent pumping. Thus there are possible applications to fast optical switching and lasing without inversion.We report an observation of transient EIT effects in the nonadiabatic regime, using a 85 Rb sample cooled in a magneto-optical trap ͑MOT͒. A three-level ⌳ system wa...

This paper presents a wide-ranging theoretical and experimental study of nonadiabatic transient phenomena in a ⌳ electromagnetically induced transparency 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 87 Rb magneto-optical trap. The results show transient probe gain in parameter regions not previously studied, and provide insight into the transition dynamics between bare and dressed states.

We show that for appropriate choices of parameters it is possible to achieve photon blockade in idealised one, two and three atom systems. We also include realistic parameter ranges for rubidium as the atomic species. Our results circumvent the doubts cast by recent discussion in the literature (Grangier et al Phys. Rev Lett. 81, 2833(1998), Imamoglu et al Phys. Rev. Lett. 81, 2836(1998) on the possibility of photon blockade in multi-atom systems.

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Interest in lossless nonlinearities has focussed on the dispersive properties of ⌳ systems under conditions of electromagnetically induced transparency ͑EIT͒. We generalize the ⌳ system by introducing further degenerate states to realize a ''chain ⌳'' atom where multiple coupling of the probe field significantly enhances the intensity-dependent dispersion without compromising the EIT condition. There has been much interest lately in the enhancement of optical nonlinearities in electromagnetically induced transparency ͑EIT͒. Most of the work has focussed on the threestate system in the ⌳ configuration, which has provided some dramatic examples of nonlinear optical effects. Examples include ultraslow ͓1͔, stopped ͓2͔ and superluminal ͓3͔ group velocities, coherent sideband generation ͓4͔, etc. All these nonlinear processes depend on the creation of coherent superpositions of the ground states with accompanying loss of absorption, and such mechanisms were described in Ref. ͓5͔. Thorough reviews of EIT and its properties can be found in Refs. ͓6,7͔.Recent investigations of nonlinear optics at the few or single-photon levels have identified four state systems where the probe field simultaneously couples two transitions in the N configuration. Examples of applications for such work include photon blockade ͓8͔ and two-photon absorptive switches ͓9͔. The classical precursors to such experiments have also been performed ͓10,11͔. Other experiments on the N scheme have been performed by É ntin et al. ͓12͔. In order to realize larger nonlinear effects, Zubairy et al. ͓13͔ suggested an extension where the more usual N configuration was extended to a system with an arbitrary ͑even͒ number of states where all the states are resonantly coupled except on the final transition where detuning is present. This scheme shows enhanced nonlinearities of not only 3 but also higher-order susceptibilities. One problem with this scheme and the standard N scheme is to do with the need to balance the required nonlinearity and decoherence in the system. To enhance the nonlinearity present in the systems it is important for the detuning of the final probe field to be minimized, however, decreasing the detuning increases the amount of the final excited state which is mixed into the coherent superposition state, resulting in an increase in decoherence and optical losses. This problem is to some extent circumvented by the absorptive switch of Harris and Yamomoto ͓9͔ by exploiting such losses, and in photon blockade by using the cavity nonlinearity to prevent absorption of the final photon. Still the increase in decoherence proves to be a difficulty in experimental precursors to these processes and causes problems in traveling wave configurations.An alternative multistate configuration for investigating EIT enhanced nonlinearities is the tripod configuration, studied recently by Paspalakis and Knight ͓14͔ and earlier considered by Morris and Shore ͓15͔. This system has many of the advantages of the N system, but by maintaining superposition states ...

We have observed clear Rabi oscillations of a weak probe in a strongly driven three-level ⌳ system in laser-cooled rubidium. When the coupling field is nonadiabatically 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. DOI: 10.1103/PhysRevA.64.055801 PACS number͑s͒: 42.50.Gy, 42.50.Md, 42.50.Hz, 32.80.Pj In the past decade there has been growing interest in the study of atomic coherence effects in multilevel atoms, especially coherent population trapping ͓1͔, electromagnetically induced transparency ͑EIT͒ ͓2͔, slow light propagation ͓3͔, and optical gain without inversion. Reviews of lasing without inversion have been given by Kocharovska and Scully ͓4͔ and more recently by Mompart and Corbalán ͓5͔. Most of this work has been in the steady-state regime and the fast picosecond pulsed regime ͓6͔, but there have been several studies of transient effects where the coherence is switched on or off rapidly in a time that is short compared to decay rates and Rabi frequencies, i.e., in the nonadiabatic regime. An early experiment by Fry et al. ͓7͔ demonstrated several transient effects in a three-level ⌳ system realized in a sodium vapor cell. Their observations included transient gain of a strong field when a weak field was switched on by a Pockels cell in the presence of incoherent pumping to the upper level, but without population inversion. Subsequently, several theoretical studies of nondegenerate three-level lambda, V, and cascade systems have predicted transient ringing of a probe beam with gain when a strong coupling beam is switched on ͓8,9͔. This predicted transient gain can occur without population inversion on the probe transition, and occurs with and without incoherent pumping. This ringing has also been explained by Vaccaro et al. ͓10͔ via stochastic wave-function diagrams. Transient ringing of a threelevel system with gain has been observed in the radiofrequency regime in nitrogen-vacancy centers in diamond samples ͓11͔ but not yet in the optical region. Since the ringing occurs at approximately the Rabi frequency of the strong field, experiments in the optical region would need to be carried out in a Doppler-free configuration or ideally in a laser-cooled sample to avoid the Doppler effects masking the coherent effects.In our previous work ͓12͔ we observed the transient approach to EIT in a cold rubidium ⌳ system in a magnetooptical trap ͑MOT͒. When the coupling field was switched on by a Pockels cell, the rapid rise in probe transparency exhibited an overshoot before settling down to the steady state. This overshoot was interpreted as the first Rabi halfcycle in the transient ringing, but it did not reach gain owing to absorption on uncoupled Zeeman transitions and twophoton dephasing effects. In the experiments reported in this paper the coupling field intensity has been increased to the point where a clear Rabi ringing cycle reaching well into gain is observ...

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