Pump Rabi Frequency Research Articles

Stimulated Raman adiabatic passage in a quantum system near a plasmonic nanoparticle

We investigate theoretically the population transfer process in a Λ-type three-level quantum system (QS) near a metallic nanosphere using the stimulated Raman adiabatic passage (STIRAP) technique. We combine density matrix quantum dynamical calculations with first-principle electromagnetic calculations, which quantify the influence of the plasmonic nanoparticle on the electric field of the pump and Stokes pulses in STIRAP as well as on the spontaneous emission rates within the Λ-type system. We study the population transfer process by varying the free-space spontaneous emission rate, the distance of the QS from the nanosphere, the polarization direction with respect to the nanoparticle surface and the relative strength of the pump and Stokes pulses used in STIRAP. We find that when the pump and Stokes fields have tangential and radial polarizations with respect to the nanosphere surface, the transfer efficiency is improved due to the increase of the decay rate of the excited state to the target state relatively to the decay to the initial state. The optimal population transfer is achieved for small interparticle distances, moderate free space spontaneous decay rate, large values of the pump Rabi frequency and small values of the Stokes Rabi frequency. When we exchange the polarization directions of the pump and Stokes fields we can still find a range of parameters where the population transfer remains efficient, but larger Stokes Rabi frequencies are necessary to overcome the increased decay rate from the excited state back to the initial state.

Electromagnetically induced transparency in a V-system with 87Rb vapour in the hyperfine Paschen-Back regime

We observe electromagnetically induced transparency (EIT) in a V-system in a thermal rubidium-87 vapour in the hyperfine Paschen-Back regime, realised with a 0.6 T axial magnetic field. In this regime energy levels are no longer degenerate and EIT features from different initial states are distinct, which we show produces a much cleaner feature than without a magnetic field. We compare our results to a model using the time-dependent Lindblad master equation, and having averaged over a distribution of interaction times, see good qualitative agreement for a range of pump Rabi frequencies. Excited state decay into both ground states is shown to play a prominent role in the generation of the transparency feature, which arises mainly due to transfer of population into the ground state not coupled by the probe beam. We use the model to investigate the importance of coherence in this feature, showing that its contribution is more significant at smaller pump Rabi frequencies.

A theoretical study of the group refractive index n g in a four-level inverted Y-type system formed by 87Rb atom – laser radiation interaction

We report a theoretical investigation of the dispersion resulting from electromagnetically induced transparency (EIT) and the associated group refractive index profiles n g of a four-level inverted Y-type system formed by the interaction of three optical fields (probe, pump and control) with 87Rb atoms. The density matrix equations are derived from the semi-classical Liouville’s equation and solved both numerically and analytically to study the coherent nonlinear optical properties of the medium. We first present the EIT, dispersion and corresponding group index profiles n g under the switch-on/off and on/off-resonance conditions of the pump and control lasers. In presence of both pump and control lasers, an enhancement of the EIT window, a sharp EIT spike and related steeper dispersion slopes are obtained at the line centre of the probe frequency detuning. The group index profiles with the variation of the strengths of individual applied optical fields are studied. The effect of the ground state decoherence rates on the group index profile is examined in detail. It is found that the manipulation of n g values and the corresponding group velocities ν g of the probe light can be easily controlled from subluminal to superluminal values or vice versa by changing the strengths of the applied fields and the ground state decoherence rates. Besides, the EIT-based ‘optical switching’ phenomenon in the medium is explained by studying the variation of the group index with the pump and control Rabi frequencies.

Hyperradiance by a stream of phase-correlated atomic dipole pairs traversing a high-Q cavity

Hyperradiance in which radiation rate exceeds that of superradiance has been theoretically investigated in various coherently-coupled emitter-field systems. In most cases, either proposed setups were experimentally challenging or the mean photon number in a cavity was limited. In this paper, with numerical simulations and analytic calculations, we demonstrate that significant hyperradiance with a large mean photon number can occur in a microlaser system, where pairs of two-level atoms prepared in quantum superposition states traverse a high-Q cavity in the presence of a pump field intersecting the cavity mode. Hyperradiance is induced when the intracavity-pump Rabi frequency is out of phase with respect to the atom-cavity coupling so that the reduction of atomic polarization by the atom-cavity coupling is compensated by the pump Rabi frequency in the steady state to maximize atomic photoemission.

Two-photon resonances, ac Stark splittings, and shifts of the resonance peaks in Doppler free absorptive lineshapes of a double-lambda type four level system

Under Doppler free condition and by using semiclassical approach, a double-lambda type four-level system coupled to two electromagnetic fields are investigated. The coupled optical Bloch equations involving the density matrix elements in steady state are solved numerically to investigate the signal lineshapes as the function of signal detuning and pump Rabi-frequencies. The on-resonant pump leads to dynamic Stark splitting. The dent in the absorption lineshape is exhibited for off-resonant pump and is a signature of two-photon resonances. The appearance of extra absorption and emission peaks in the computed lineshapes are attributed by the nonlinear polarizations and hence the spontaneously generated coherences.

Mechanical squeezing of the tripod-type four-level atom-assisted optomechanical system

Quadrature squeezing of a mesoscopic mechanical oscillator is investigated in a driven hybrid optomechanical system with a membrane-in-middle configuration containing a tripod-type four-level atom on either side of the membrane. We analyze in detail the influence of the coupling constant between cavity field and atom, amplitude of pump field, cavity pump detuning and Rabi frequency of classical field on the squeezing of the position quadrature of the vibrating membrane. The results show that the mechanical squeezing can be controlled by choosing the evolved parameters and initial state of atom, appropriately. Also, it is shown that a noticeable amount of squeezing can be obtained by increasing the amplitude of the classical pump field and therefore effective coupling constant. More over, we investigate that such a system can lead to a larger squeezing than the case with Λ-type three-level atom.

Study of Atomic Populations, Electromagnetically Induced Transparency, and Dispersive Signals in a λ-Type System Under Various Decoherence Effects

We have theoretically studied the atomic populations, electromagnetically induced transparency (EIT), and dispersion in a three-level Λ-type system. The density matrix equations are set up with regard for the relaxation of populations of the ground states, and the optical Bloch equations are solved analytically in the weak probe field approximation. Decoherence effects in the ground and excited states on the EIT line shape and dispersive signals are studied, and it is found that the EIT line width increases and the peak height decreases, as the decoherence rates increase in the ground and excited states. On the other hand, we have observed that the dispersive signals are steeper and of high contrast for the lower decoherence rates in the ground and excited states. We have also analyzed the variations of atomic populations of the energy levels at the pump Rabi frequency, as well as the decoherence rate in the ground state.

Pulse delay and group velocity dispersion measurement in V-type electromagnetically induced transparency of hot atom

Pulse delay with the group velocity dispersion (GVD) characteristics was studied in the V-type electromagnetically induced transparency in the hyperfine levels of atoms with a closed system configuration. The phase coherency between the pump and the probe laser beams was maintained. We studied the pulse delay and the GVD characteristics with the variation of the pump Rabi frequency taking optical density (OD) as a parameter. We observed a maximum of 268 ns pulse delay for 21.24 MHz pump Rabi frequency at OD 5.04 of the Rb vapor cell. For a better understanding of the experimental results, we have derived an analytical solution for the delay characteristics considering the thermal averaging. The analytical solution was derived for a three level V-type system. The theoretical plots of the delay and the GVD show the same characteristics as we observed in the experiment. This analytical approach can be further generalized for the higher level schemes to calculate different quantities such as susceptibility, group velocity delay or GVD characteristics.

Observation and theoretical simulation of dispersive properties of an electromagnetically induced transparent 87Rb atomic medium

The dispersive properties of 87Rb atomic medium in electromagnetically induced transparency (EIT) have been studied experimentally as well as theoretically. To measure the dispersion signal, a balanced homodyne detection technique was used by forming a Mach–Zehnder interferometer. We studied the system in a Λ-type configuration. From the slope of the dispersive EIT signal, the group index (ng) of the atomic medium, the group velocity () and the time delay () of the light wave through the atomic medium were calculated. We measured the group index of the atomic medium from the dispersion signal and observed that it non-linearly depends on the pump power. This non-linearity signifies that to achieve the maximum reduced group velocity, optimization of the pump power is needed. We got the maximum reduction in the group velocity of the probe beam as m s−1. The corresponding time delay was ns. To support our experimental observation, we have performed a theoretical simulation by taking the semi-classical approach of density matrix formalism of a Λ-type three level system. To get the probe response we solved the optical Bloch equation analytically assuming the Lorentzian velocity distribution of the atom. We have observed that our analytical solution matched exactly with the numerical solution. Our experimental observation of non-linear variation of the group index with the pump Rabi frequency matched quite well with both of our numerical and analytical simulations.

Slowing 80-ns light pulses by four-wave mixing in potassium vapor

We experimentally and theoretically study propagation of 80-ns Gaussian-like probe pulses in hot potassium vapor under conditions of four-wave mixing (FWM). The atomic scheme for FWM is off-resonant, double-$\mathrm{\ensuremath{\Lambda}}$ atomic scheme, with pump and probe photons, mediated in the K vapor, generating new probe and conjugate photons. We define the subset of FWM parameters, one-photon pump detuning, two-photon pump-probe Raman detuning, vapor density, the pump Rabi frequencies, when slowed pulses exit the vapor are also Gaussian-like. When Gaussian-like pulses exit the cell we are able to compare theoretical and experimental results for fractional delays and broadening for the probe and conjugate. We have obtained fractional delays above 1. Results of the model are compared with the experiment, with and without the model of Doppler averaging, when the atom velocity distribution is divided into different number of groups. We analyze possible causes for pulse broadening and distortion of slowed probe pulses and show that they are the result of quite different behavior of the probe pulse in the FWM vapor. Besides presenting the first results of slowing 80-ns probe pulses, this work is a useful test of the numerical model and values of parameters taken in the model that are not known in experiments.

Temporal optical memory based on coherent population and two-photon coherence oscillations

We consider the ${F}_{g}=1\ensuremath{\rightarrow}{F}_{e}=1$ transition between the ground and excited hyperfine levels in alkali-metal vapor interacting with $\ensuremath{\sigma}$ linearly polarized control and probe fields whose polarizations can be either parallel or perpendicular to each other. We develop a matrix formulation that allows a solution of the Bloch equations to all orders in the pump and probe Rabi frequencies. Using this formalism, we calculate the steady-state probe absorption spectrum, the coherent population oscillations (CPOs), and two-photon coherence, in the absence (degenerate case) and presence (nondegenerate case) of a longitudinal magnetic field. We then calculate the probe storage when the pump is switched off and on again. We are particularly interested in whether the probe regains its original temporal shape when the pump is switched on again for the case of identical pump and probe frequencies. We show that, in the nondegenerate case, the restored probe does not regain its original shape whereas, in the degenerate case, the original shape is restored. This can be explained by considering the relative magnitudes of the CPOs which do not remember the temporal shape of the probe and the two-photon coherence oscillations which store the probe shape when the pump is switched off, as in electromagnetically induced transparency memories. In the nondegenerate case, the CPOs are much stronger than the two-photon coherence oscillations whereas, in the degenerate case, they are of similar magnitudes. Thus it is the two-photon coherence oscillations that are responsible for the restoration of the temporal shape of the probe in the degenerate case.

Asymmetric light diffraction of an atomic grating with PT symmetry.

Cold atoms trapped in one-dimensional optical lattices and driven to the four-level N configuration are exploited for achieving an electromagnetically induced grating with parity-time-symmetry. This nontrivial grating exhibits unidirectional diffraction patterns, e.g.,with incident probe photons diffracted into either negative or positive angles, depending on the sign relation between spatially modulated absorption and dispersion coefficients. Such asymmetric light diffraction is a result of the out-of-phase interplay of amplitude and phase modulations of transmission function and can be easily tuned via optical depth, probe detuning, pump Rabi frequencies, etc.

Tunable amplification and absorption properties in double-Λ system of GaAs/AlGaAs multiple quantum wells

We study the optical amplification and absorption properties in a double-Λ four level system of GaAs/AlGaAs multiple quantum wells (MQWs) under realistic experimental conditions. The amplification and absorption responses of two weak fields can be achieved by adjusting the relative phase, the probe detuning, and the two pump Rabi frequencies appropriately. The investigation is much more practical than its atomic counterpart because of its flexible design and the wide adjustable parameters. It may provide a new possibility in technological applications for the light amplifier working on quantum coherence effects in MQWs solid-state system.

Analytical description of the Stokes coherent cooperative Raman scattering by a subwavelength sample

The present article is aimed at an analytical description of Stokes coherent cooperative Raman scattering by three-level quantum systems confined in a ball with a diameter much smaller than the Stokes wavelength. It is shown that if the pump electric field is strong enough to neglect the influence of the ball self-radiation on the dynamic of the ground to the second excited state transition, then the inverse pump Rabi frequency is much smaller than the duration of the radiated Stokes pulse. It is found that in this case and under the assumption of a resonant pump the problem has an analytical solution. The latter demonstrates that the emitted Stokes pulse has a time-profile two times lower and longer than that of a superadiant pulse from a subwavelength sample of initially fully inverted two-level systems. The obtained analytical solution may be used, e.g. for testing the fidelity of numerical models of coherent cooperative Raman scattering in the limiting domain of parameters where it is valid.

Analytical studies on pump-induced optical resonances in an M-type six-level system

In the domain of semiclassical formulation and for the Doppler-free atom–field interaction, we construct the optical Bloch equations involving an M-type six-level system coupled to two pump fields and a probe field. The response of the system is probed for different pump-induced transitions in double and triple-resonance situations. In order to obtain the coherent lineshapes (absorptive and dispersive), we use the usual perturbation method for obtaining the approximate analytical solutions to these coupled optical Bloch equations for the density matrix elements. The interferences between the probability amplitudes for different energy levels (dipole allowed and dipole forbidden) are taken care of. For off-resonance pump positions, the linewidths of the three probe transitions are insensitive to the pump Rabi frequencies. On the other hand, the shifts of the three resonance peaks are extremely sensitive to the pump Rabi frequencies. However, for on-resonance pump conditions, the sensitivities of pump Rabi frequencies on the linewidths of the resonance peaks and on the shifts of the resonance peak positions are opposite to those of their off-resonance counterparts. In particular, we have shown the asymmetric and symmetric Rabi splittings under different physical conditions, for non-zero and near-zero probe detuning, respectively. The Rabi splitting under triple-resonance conditions, significantly, modifies the dispersive lineshape at the centre of the absorption line. The two- and three-photon absorptions are also reported for different off-resonant pump positions.

Electromagnetically induced absorption due to transfer of population in degenerate two-level systems

We predict the occurrence of electromagnetically induced absorption (EIA) in cycling degenerate two-level transitions where ${F}_{e}={F}_{g}+1$ and ${F}_{g}>0$, interacting with pump and probe lasers with the same polarization. The EIA is due to transfer of population (TOP) between the Zeeman levels of the ground hyperfine state, rather than transfer of coherence (TOC) which occurs for perpendicularly polarized lasers. We model EIA-TOP using a double two-level system (TLS) which we compare with the four-level $N$ system, which models EIA-TOC. When the pump intensity is low, both models give an EIA peak at line center. The effect of introducing phase-changing collisions is studied, in the presence and absence of Doppler broadening, for both the double TLS and $N$ systems. In the presence of phase-changing collisions, the central EIA peaks are narrowed in both models and persist to higher pump Rabi frequencies than in the absence of collisions. In the double TLS, in the presence of Doppler broadening, the central EIA-TOP peak becomes narrower and does not develop a dip in its center, in contrast to the $N$ system. The central dip that appears in the Doppler-broadened EIA-TOC spectrum can be wiped out by adding phase-changing collisions. We demonstrate that EIA-TOP can be obtained for realistic atomic transitions interacting with lasers that have the same polarization.

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.

Positive and negative dispersion in a three-level Λ system driven by a single pump

We extend our previous study of a nearly degenerate Λ three-level system that exhibits population trapping when driven by a single pump and produces an absorption or gain doublet in the probe absorption spectrum. In particular, we show that the probe dispersion is positive or negative between the doublet lines, and can survive Doppler broadening. For certain values of the pump Rabi frequency, the sign of the dispersion can be changed by altering the ratio of the splitting between the lower levels to the Doppler width.

Transient hole-burning for systems with a noncorrelated frequency exchange

The exact solution of the transient hole-burning (THB) shape has been obtained for systems with a noncorrelated spectral exchange. The THB shapes have been studied for various values of pump Rabi frequency χ/2 π, time duration and pump–probe time separation. It is shown that the correlated line is dominant in the slow spectral diffusion limit, and it decays with 1/e time of the correlation time τ c; in the fast limit, the hole is mainly determined by the width of the equilibrium frequency distribution a. When χ→0, the linewidths are ∼3/ πτ c and 2 a/ π in the slow and fast limit, respectively. The model fails to explain the THB experiments in ruby. However, it is more suitable to describe the FID behaviors under the same experimental condition [V.S. Malinovsky, A. Szabo, Phys. Rev. A 55 (1997) 3826].

Dephasing- and field-induced effects in hole burning

In this paper, we study the probe absorption profile of a two-level system subjected to an arbitrary strong pump field. By using a three-component solution developed earlier, we find that the lineshape can be understood in terms of an induced Rabi frequency, which is dominated by the dephasing-induced effect when the pump intensity is in the intermediate regime or below, and by the field-induced effect when the pump is strong. With the assumption of a large inhomogeneous broadening, we calculate the holewidth as a function of the pump intensity. We find, quite unexpectedly, that the holewidth, even in a strongly dephased system, approaches the pump Rabi frequency at the high pump intensity limit.