Perturbative and nonperturbative processes in adiabatic population transfer

With the help of superadiabatic techniques for quantum systems depending slowly on time, we demonstrate how the total transition amplitude, tracked in time in the usual adiabatic basis, can be decomposed into a perturbative part consisting of terms proportional to powers of the adiabaticity parameter, and a nonperturbative component. The interference of both components underlies the oscillations that accompany transitions in the adiabatic basis. Whereas for traditionally considered systems the final nonadiabatic transition probability is determined by the nonperturbative part alone, this is no longer correct for models describing stimulated Raman adiabatic passage (STIRAP). We explain the recently discovered breakdown of the Dykhne-Davis-Pechukas formula on general grounds, and provide simple, but accurate approximations for transition amplitudes in STIRAP systems. Received: 22 January 1998 / Revised: 17 March 1998 / Accepted: 31 March 1998     

Adiabatic population transfer in multistate chains via dressed intermediate states

The well-known process of stimulated Raman adiabatic passage (STIRAP) provides a robust technique for achieving complete population transfer between the first and last state of a three-state chain, with little population, even transiently, in the intermediate state. The extension of STIRAP to general N-state chainwise-linked systems continues to generate interest. Recently Malinovsky and Tannor (Phys. Rev. A 56, 4929 (1997)) have shown with numerical simulation that a resonant pulse sequence, which they term “straddle STIRAP”, can produce (under appropriate conditions, including specific pulse areas) complete population transfer with very little population in intermediate states. Their proposal supplements a pair of counterintuitively ordered delayed laser pulses, driving the first and last transition of the chain and corresponding to the pump and Stokes pulses in STIRAP, with one or more additional strong pulses of longer duration which couple the intermediate transition(s) and overlap both the pump and the Stokes pulses. In this paper, we modify the “straddling” Malinovsky-Tannor pulse sequence so that the intermediate couplings are constant (and strong), at least during the times when the pump and Stokes pulses are present, and the intermediate states therefore act as a strongly coupled subsystem with constant eigenvalues. Under this condition, we show that the original N-state chain is mathematically equivalent to a system comprising N-2 parallel -transitions, in which the initial state is coupled simultaneously to N-2 dressed intermediate states, which in turn are coupled to the final state. The population transfer is optimized by suitably tuning the pump and Stokes frequencies to resonance with one of these dressed intermediate states, which effectively acts as the single intermediate state in a three-state STIRAP-like process. We show that tuning to a dressed intermediate state turns the system (for both odd N and even N) into a three-state system - with all of the properties of conventional STIRAP (complete population transfer, little transient population in the intermediate states, insensitivity to variations in the laser parameters, such as pulse area). The success of the tuning-to-dressed-state idea is explained by using simple analytic approaches and illustrated with numerical simulations for four-, five-, six- and seven-state systems. Received: 17 April 1998 / Accepted: 15 June 1998     

Direct evidence of a magnetization transfer between laser-polarized xenon and protons of a cage-molecule in water

In a dedicated experimental setup, we directly prepare liquid-state NMR samples containing laser-polarized xenon with nuclear polarization larger than 5% at pressures up to 4 bars. Coating of the NMR tube surface allows us to increase the self-relaxation time of xenon in the gaseous phase to approximately 4.5 hours. Using a modified SPINOE pulse sequence, we present the first direct detection of a regioselective proton signal enhancement of a molecule -cyclodextrin) dissolved in water resulting from cross-polarization between laser-polarized xenon and protons. Received 16 March 2000 and Received in final form 22 May 2000     

Precise measurement of hyperfine coupling in CH F based on nuclear spin conversion

A new method is proposed for the experimental determination of the hyperfine coupling in molecules. The method is based on the level-crossing effect in the spin isomer conversion in alternating electric fields. An experiment performed with the ¹³CH₃F molecules has revealed the strength of the off-diagonal in K () nuclear spin-spin coupling kHz, which is only by kHz larger than the theoretical value calculated on the basis of the molecular structure. Received 25 January 2000 and Received in final form 11 May 2000     

Nuclear spin conversion in CH F induced by an alternating electric field

The nuclear spin conversion in CH₃F molecules subjected to an alternating electric field was investigated experimentally. The conversion rate was found to be almost unaffected by low electric fields ( V/cm) but sharply increased tenfold when the electric field amplitude exceeds the values ( V/cm) sufficiently high to produce crossings of the ortho and para states of the molecule. A theoretical model for the molecular conversion in alternating electric field was developed. The results of the experiment were found to be in a good agreement with the theory. Received 23 July 1999 and Received in final form 7 September 1999     

Two strong nonlinearity regimes in cold molecule formation

Two distinct strongly non-linear scenarios of molecule formation in an atomic Bose-Einstein condensate (either by photoassociation or Feshbach resonance) corresponding to large and small field detuning are revealed. By examining arbitrary external field configurations, we show that the association process in the first case is almost non-oscillatory in time while in the second case the evolution of the system displays strongly pronounced Rabi-type oscillations. We construct highly accurate approximate solutions for both limit cases. We show that at strong coupling limit the non-crossing models are able to provide conversion of no more than one third of the initial atomic population. Finally, we show that for constant-amplitude models involving a finite final detuning the strong interaction limit is not optimal for molecule formation.     

Generation of multiple orientation in an alkali vapour by intermediate optical pumping

Summary The generation of hyperfine, dipole and quadrupole orientations in an alkali vapour by means of optical pumping withD ₁ σ-polarized light is studied in an intermediate pumping approximation. Pumping equations are explicitly given for any alkali vapour in the case of white-light pumping and for cesium vapour (I=7/2) in the case of pumping with nonuniform spectrum light. The dependence of the steady-state multipole orientation on the pumping and relaxation characteristic parameters is discussed.

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Riassunto Si studia la generazione di orientamenti iperfini, dipolari e quadrupolari in vapore alcalino mediante pompaggio ottico con luce σ-polarizzataD ₁ in un'approssimazione di pompaggio intermedio. Le equazioni di pompaggio sono date esplicitamente per ogni vapore alcalino nel caso di pompaggio di luce bianca, e per vapore di cesio (I=7/2) nel caso di pompaggio con luce spettrale non uniforme. Si discute la dipendenza dell'orientazione multipolare dello stato stazionario dal pompaggio e dai parametri caratteristici di rilassamento.

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Резюме Исследуется получение сверхтонких дипольной и квадрупольной ориентации в щелочных парах с помощью накачкиD ₁ σ-поляризованным светом в приближении промежуточной накачки. В явном виде записываются уравнения накачки для любых щелочных паров в случае накачки белым светом, а для паров цезия (I=7/2) в случае накачки светом с неравномерным спектром. Обсуждается зависимость стационарной мультипольной ориентации от накачки и характерных параметров релаксации.

     

Nonlinear Hanle effect in Cs vapor under strong laser excitation

We report results of a theoretical and experimental study of the ground state nonlinear Hanle effect under strong laser excitation. It is shown that besides the well-known zero-magnetic field suppression of absorption on F _g = F→F _e = F - 1 transitions caused by population trapping, an optical pumping induced enhanced absorption occurs on F _g = F→F _e = F + 1 transitions for small B-fields. The latter effect becomes more pronounced for high F values. The experiment with atomic vapor of Cs (D₂ line, F _g = 4) confirms an increase of the spectrally unresolved fluorescence yield at zero magnetic field and 600 mW/cm² laser intensity by 9% or 42%, when excitation occurs with linearly or circularly polarized light, respectively. The results of the experiment agree with numerical simulation studies using equations of motion for a density matrix. Received 24 November 2001 / Received in final form 25 March 2002 Published online 24 September 2002     

Velocity selective optical pumping and repumping effects with counter and copropagating laser radiations for D<Subscript>2</Subscript> lines of rubidium

The effects of a strong control or pump laser, counter propagating or copropagating with the probe beam, on the probe absorption spectra of ⁸⁵Rb and ⁸⁷Rb-D₂ transitions have been investigated inside a room temperature Rb vapour cell. In both cases a set of strong velocity selective resonance dips are observed at different velocities. Their movements across the Doppler broadened probe absorption profile have been studied for different lock frequencies of the control laser. These spectra are modified by optical pumping effects due to the presence of another hyperfine component of the ground state. A repumping laser, from the dark hyperfine component of the ground level transfers almost 75% of the atoms from the dark state to the pump probe cycle hence reducing the optical pumping effect. A numerical simulation is done to explain the observed spectra. The effect of a control laser on the Lamb dip spectrum of the probe laser has also been investigated. The control beam is used to improve the strength of a weak hyperfine dip on the Doppler broadened probe spectrum. The strength of the hyperfine dip increases by a factor of 3.2 in presence of the control laser. The observed dips show that pump-probe spectroscopy can be used as velocity selectors of atoms.     

Two body loss rate in a magneto-optical trap of metastable He

We have measured the two body loss rate in a magneto-optical trap containing triplet metastable He atoms. We find a rate constant cm³/s at a -8 MHz detuning, with an uncertainty of a factor 2. This measurement is in disagreement with a recent experiment which measures the absolute, ion-producing collision rate, but agrees with several other published measurements. Received 20 April 1999 and Received in final form 12 July 1999     

Floquet theory for short laser pulses

We develop adiabatic perturbation theory for quantum systems responding to short laser pulses, with or without a frequency chirp. Our approach rests on lifting the time-dependent Schr?dinger equation to an extended Hilbert space, then applying standard perturbational techniques to Floquet states in this extended space, and finally projecting back to the physical Hilbert space. The same strategy also allows us to construct superadiabatic bases for monitoring the quantum evolution in the course of a pulse. These bases provide a diagnostic tool for improving the efficiency of pulse-induced population transfer. The formalism is applied to the selective excitation of molecular vibrational states by chirped laser pulses, which exploit either successive single-photon resonances or a multiphoton resonance, and by a STIRAP-like process. Received: 23 June 1998 / Revised: 18 August 1998 / Accepted: 25 August 1998     

Optical pumping and coherence effects in fluorescence from a four level system

An effective four-level system around the D2 line of ⁸⁵Rb at room temperature, is experimentally investigated by fluorescent studies under the action of two driving fields L1 and L2. This system exhibits unique features in fluorescence as a function of frequency separation between L1 and L2. In particular, at two-photon resonance, when the Rabi frequency of L1 exceeds that of L2, signatures of Electromagnetically Induced Transperancy effect (EIT) arising from the three-level Λ sub-system is present as a sub-natural dip in fluorescence from the fourth level. At comparable strengths of L1 and L2 the fluorescence features indicate a regime, where the effects arising from optical pumping and EIT effect due to ground hyperfine level coherence coexist. We see in the coexistence regime, saturation effects arising from difference frequency crossing (DFC) resonances and optical pumping around the EIT window. At low strengths of L1, all signs of coherence vanishes from the system and the fluorescent features result from incoherent optical pumping through the Autler-Townes split states of the excited state hyperfine levels, which are split due to the stronger L2 laser. The dominant role of the L1 laser in creating a robust transparency signal even in the presence of an off-resonant excitation is brought out. The results are supported by density matrix calculations.     

Investigation of sub-Doppler cooling effects in a cesium magneto-optical trap

We present an investigation of sub-Doppler effects in a cesium magneto-optical trap. First, a simple one-dimensional theoretical model of the trap is developed for aJ _g = 1 J _e = 2 transition. This model predicts the size of the trapped atom cloud and temperature as a function of laser intensity and detuning. In the limit of small magnetic field gradients, the trap temperature is found to be equal to the molasses temperature and a minimum size for the trap is calculated. We then describe several experiments performed in a three-dimensional cesium trap to measure the trap parameters, spring constant, friction coefficient, temperature and density. Whilst the temperature of the trapped atoms is found to be equal to the molasses temperature, in agreement with theory, the trap spring constant is found to be two orders of magnitude smaller than the one-dimensional prediction, a value close to that predicted by Doppler models. The maximum density is found to be on the order of 10¹² atoms/cm³ or one atom per optical wavelength on average. When the number of trapped atoms becomes large, the temperature begins to increase dramatically. This excess temperature depends in a very simple way on the atom number, laser intensity and detuning, suggesting that its origin lies in multiple photon scattering within the trap.     

Dynamic control of the entanglement in the presence of the time-varying field

The interactions between a two-level atom and a field with a time-varying frequency have been investigated. The two typical cases, the frequency of the field varying with time in the forms of sine and rectangle, have been considered. The dynamic behavior of the atom-field entanglement is investigated numerically as function of time. A number of novel phenomena are discovered and discussed. The sine modulation of the field frequency can help to realize and stabilize the degree of the atom-field entanglement at high level. The influence of the rectangular frequency modulated field on the atom-field entanglement indicates that the entanglement is more sensitive to the detuning than the correlation between different Rabi oscillations. Not only the sine field frequency modulation but also the rectangular field frequency modulation is favorable to improve, enhance and stabilize the degree of the atom-field entanglement.     

Efficient population transfer by delayed pulses despite coupling ambiguity

In traditional schemes of multilevel multilaser excitation, each laser pulse interacts with only one pair of states, and the rotating wave approximation (RWA) is applicable. Here we study the population transfer process in a three-state system when each of the two lasers interacts with each of the pair of states and when the Rabi frequencies characterizing the interaction strengths of the system are comparable to or larger than the difference of the transition frequencies. We show that complete and robust population transfer is possible under conditions more general than those hitherto considered necessary for stimulated Raman adiabatic passage (STIRAP) or for successive π pulses. Using adiabatic Floquet theory we show that successful population transfer can be interpreted as adiabatic passage by means of a transfer state which connects the initial and final states. The Floquet picture offers a convenient interpretation of the population transfer as accompanied by multiple absorption of photons from or emission into the laser fields.     

Spontaneous emission from a three-level atom embedded in an anisotropic photonic crystal

We study the spontaneous emission properties of a V-type three-level atom embedded in a photonic crystal with the anisotropic dispersion relation. We show that the localized field can disappear and the diffusion field can become intense in some regions. This originates from no singularity of the density of states. The quantum interference leads to oscillatory, quasi-oscillatory or complete decay behavior of population. The complete decay can also be realized in certain condition without depending on the initial state. Received 9 April 2000 and Received in final form 1st August 2000     

Heating of cold cesium atoms by blue-detuned laser radiation

Received: 12 March 1997/Revised version: 30 July 1997     

Landau-Zener transition of a two-level system driven by spin chains near their critical points

The Landau-Zener (LZ) transition of a two-level system coupling to spin chains near their critical points is studied in this paper. Two kinds of spin chains, the Ising spin chain and XY spin chain, are considered. We calculate and analyze the effects of system-chain coupling on the LZ transition. A relation between the LZ transition and the critical points of the spin chain is established. These results suggest that LZ transitions may serve as the witnesses of criticality of the spin chain. This may provide a new way to study quantum phase transitions as well as LZ transitions.     

Spontaneous emission from a ladder three-level atom in anisotropic photonic crystals

We investigate the spontaneous radiation from a ladder three-level atom embedded in a three-dimensional anisotropic photonic crystal with an external driving field. The properties of the spontaneous emission are dependent strongly on the relative position of the middle level from the band edge. Due to the Autler-Townes splitting by the action of the driving field, the external driving field can also affect the properties of the spontaneous emission. The population exchanged between the upper and the middle levels decreases as the detuning of the external driving field frequency from the corresponding transition frequency increases. The properties of the emission field can be changed or so much as controlled by choosing suitable intensity of the external driving field. The emission spectrum is more complex, and dependent on the location of the observer in this case.