Research highlights

Dressed state manipulation

Teams: Riga, Vilnius, St. Petersburg, Novosibirsk

Researchers involved

Key ER and ESR staff of Riga, Vilnius, St. Petersburg and Novosibirsk teams. In course of the project new PhD students join the teams.

Scientific highlights of Dressed state manipulation

Engineering of the selection rules utilizing “artificially” forbidden transitions

Using the theoretical models developed during the previous reporting period to describe the formation of dark states upon laser coupling of three-level systems with hyperfine structure, extensive numerical simulations have been performed to understand the evolution of dressed state energies upon variation of Rabi frequency, in particular for the case of laser coupling of the 3p and 3d states of atomic sodium that are targeted in experiments that probe the 3p-3d coupling by a weak laser field on the 3s-3p hyperfine transitions. The aim is to correctly predict, interpret, and assign the rich spectral features observed upon coupling of hyperfine multi-sublevel systems. The selection rules for transitions between different hyperfine magnetic sub-levels cause different coupling patterns. Once the variation of dressed state energies is established, it is up to detailed numerical experiments to establish the observed spectral features and to unambiguously identify each spectral component upon variation of the coupling Rabi frequency. These studies have led to an interesting observation: in Autler-Townes type of experiments some hyperfine components can be excited via a number of two-photon paths, which can lead to a destructive interference between the respective probability amplitudes and hence to creation of ‘artificially’ forbidden transitions. Such destructive interference is the reason for unexpected singlet structures that are observed in the excitation spectra. Part of these results have been reported in [Proceedings of St. Petersburg state university: series on physics, 4:157-160, 20131].

The finding of “artificially” fobidden transitions has been utilized to on an exemplary demosntration of hyperfien excitstion cortrol on 3S1/2(F′′=1, 2) –> 3P3/2 –> 5S1/2 excitation scheme. The selection rules for transitions between different HF magnetic sub-levels and destructive interference between a number of the involved partial two-photon pathways (with varying intermediate HF levels) have been combined to create an artificial selection rule DeltaF=0 for the two-photon transition 3S1/2(F′′)–> 5S1/2(F). Effectivley this example means that ‘artificially’ forbidden transitions and destructive interference of multiple excitation paths are tools that can de used to “engineer” the selection rules in many-photon interactions, e.g., to selectively address and manipulate unresolved HF components of atoms and molecules.

Cost-efficient optical dipole traps by multimode fiber lasers.

Multimode fiber lasers have been shown to be suitable as a cost-efficient solution for the formation of optical dipole traps (ODTs). Usually, atoms are prepared in the lower-energy hyperfine state (i.e. the state of |F=1 for Rb atoms). However, the use of multimode fiber lasers, with availability of suitable frequency combinations within the broad bandwidth of the laser emission profile, can drive the two-photon Raman transition that optically pumps the population out of |F=1 and leads to a significantly increased population of atoms in the state of |F=2 (i.e. the higher-energy hyperfine state of Rb atoms). This process is followed by the hyperfine-state-changing collision back to |F=1 whereby the excess energy is converted into translational motion of atoms that results in to increased trap loss. We have demonstrated that two-photon Raman transitions and hyperfine-state-changing collisions can be inhibited if the atoms are prepared in the single Zeeman sublevel of |F=2,m=2 (or |F=2,m=2) and an auxiliary magnetic field is applied. Joint paper of Riga and Hsinchu teams has been accepted for the publication in J. Opt. Soc. Am. B.

Retrieval of dark state populations in optical pumping experiments.

Studies of resonant laser excitation of a slow beam of Cs atoms in a very long interaction time limit showed that ratios of excitation signals of the 6P state detected upon excitation of the (i) F”=4–>F’=5 and F”=4–>F’=4 transitions, and (ii) F”=4–>F’=4 and F”=4–>F’=3 transitions, as a function of the exciting laser power exhibit unexpected features. The analysis lead to the conclusions that (i) the traditional simulations of optical pumping in the weak excitation limit grossly fail to reproduce the experimental findings, and (ii) accurate simulations of complete time-dependent density matrix equations of are required to interpret the observations, whereby one can distinguish four stages of excitation depending on how strong is the laser power:

  • Linear stage in the wing of the laser intensity profile;
  • Saturation stage – leads to notable population deletion of the initial state for open level systems;
  • Intermediate stage – accumulation of population in “dark” or “bright” Zeeman sublevels;
  • Autler-Townes stage – mixing of hyperfine states and population retrieval from the “dark” sublevels.

This study demonstrates that experiments dealing with trapped atoms and cold atom beams must be wary that the very long atom-light interaction times typical to those conditions can lead to complicated population dynamics that affects the HF level populations in intuitively unpredictable way.

Storage of light

Teams: Vilnius, Hsinchu

Researchers involved

Key ER and ESR staff of Vilnius and Hsinchu teams. In course of the project new PhD students join the teams.

Scientific highlights of Storage of light

Control of superluminal light by multiple laser fields

The collaboration of Vilnius, St. Petersburg and Riga teams on studies superluminal light has been continued in year 3 and was concluded with the submission of a joint paper which was published in Phys.Rev.A in 2014. The main idea here is to manipulate the medium by coherent laser control fields in order to achieve a group velocity for the probe signal fields larger than speed of light via dispersion control of the medium. Earlier approaches to achieving superluminal light used only one probe field. In our study we proposed and described an alternative scheme for two-component superluminal light, which makes use of two probe fields and two or four pump fields. The main advantage of our scheme is the flexibility in controlling the two superluminal pulses by changing parameters such as power and detunings of the gain doublets. Intriguingly, if only one probe field is incident (a seed field), then the second field will be created and will appear at the end of the atom cloud before the main primary peak will enter.

Electromagnetically induced transparency and slow light in quantum degenerate atomic gases

Electromagnetically induced transparency (EIT) and properties of slow light in ultracold Bose and Fermi gases have been studied systematically. These studies reveal very different properties from those foreseen by the classical theory, which assumes frozen atomic motion. For example, the speed of light inside the atomic gases can be changed significantly near the Bose–Einstein condensation temperature, while the presence of the Fermi sea can destroy the EIT effect even at zero temperature. From an experimental point of view, such quantum EIT property is mostly manifested in the counter-propagating excitation schemes in either the low-lying Rydberg transition with a narrow linewidth or in the D2 transitions with a weak coupling field. We further investigated the interaction effects on the EIT for a weakly interacting Bose–Einstein condensate, showing an inhomogeneous broadening of the EIT profile and nontrivial change of the light speed due to the quantum depletion other than mean-field energy shift. This work has been published in [J. Opt. Soc. Am. B 30, 2855 (2013)].

Spinor slow light in the double-tripod system and its applications

Theoretical description of the spinor slow light proposed by Prof. Juzeliūnas’ group in Vilnius has been carried out for an actual experimental scheme at Prof. Yu’s group in Hisnchu. In this double-tripod experiment, we use five energy levels, driven by two probe and four coupling fields. There are two coupled processes of four-wave mixing (FWM) in the system. The probe field 1 can therefore generate the probe field 2 through this FWM mechanism. The amount of energy transferred from the probe pulse 1 to the probe pulse 2 depends on the two-photon detuning among the coupling fields. With only the probe pulse 1 appearing in the input, we measured transmissions of the output probe pulses 1 and 2 versus the two-photon detuning. Oscillation between the two probe components demonstrating the spinor nature was observed for first time. This double-tripod system, which behaves very much like the neutrino oscillation, enables us to transfer energy from one light pulse to another with high efficiency. The system can also be employed as a sensitive interferometer and in the application of quantum memory for qubits of the superposition state of two frequency modes. We also experimentally demonstrated a possible application of the double tripod scheme as quantum memory/rotator for the two-color qubit. Our work opens up a new direction in the EIT/slow light research, which may result in novel applications in quantum information manipulation, precision measurement and nonlinear optics. The results have been published in Nature Commun. 5, 5542 (2014).

Chip-scale clocks

Teams: Novosibirsk, Vilnius, Hsinchu

Researchers involved

Key ER and ESR staff of Novosibirsk, Vilnius and Hsinchu teams. In course of the project new PhD students join the teams.

Scientific highlights of Chip-scale clocks

Three-photon laser excitation of cold Rb Rydberg atoms in a switched MOT

The work has been done on narrowing the line widths and on frequency stabilization of the three cw lasers in the scheme of three-photon excitation 5S–>5P–>6S–>nP of cold Rb atoms to the Rydberg states nP (n=30-100). The external-cavity diode laser at 780 nm, telecom DFB laser at 1367 nm, and Ti-Sa laser are used. We have also performed the experiments on spectroscopy of three-photon excitation 5S–>5P–>6S–>nP of cold Rb Rydberg atoms in a magneto-optical trap (MOT) being switched off. At appropriately high Rabi frequencies of the intermediate single-photon transitions (all detuned by +/-92 МHz), we observed a narrow peak (4-5 MHz wide) of coherent three-photon excitation, while the peak of incoherent three-step excitation at zero detuning was suppressed and experienced a strong power splitting due to ac Stark effect on the 6S state (Autler-Townes effect). Comparison with numerical simulations has shown a good agreement between experiment and theory, taking into account the measured line widths of the lasers.

Quantum logic gates with mesoscopic atomic qubits based on dipole blockade

We have developed novel schemes to perform quantum logic gates with mesoscopic atom ensembles which are suitable to implement one-way quantum computation. A quantum register can be represented by a two-dimensional array of optical dipole traps where each site is loaded by random number of atoms. Single- and two-qubit gates are performed using the developed by us earlier method of deterministic excitation of single Rydberg atoms and the newly developed method to compensate for the geometric phase incursion of the collective wave function. Dipole blockade is used for encoding the quantum information in the collective states of atom ensembles and for implementing two-qubit gates.

Jaynes-Cummings dynamics in mesoscopic ensembles of Rydberg-blockaded atoms

Mesoscopic ensembles of interacting ultracold atoms are created by loading the atoms into optical dipole traps or optical lattices. Long-range interactions between Rydberg atoms in the ensemble lead to the effect of Rydberg blockade when not more than one atom could be excited into a Rydberg state by a narrow-band laser radiation. In general, the number of atoms in optical traps is random and is commonly described by the Poissonian statistics. We have shown theoretically that strongly interacting mesoscopic Rydberg ensembles with random and unknown number of atoms, which are coupled to a classical electromagnetic field, display the Jaynes-Cummings-type dynamics of single-atom laser excitation. The collapses and revivals of collective Rabi oscillations between Dicke states of the atomic ensemble result from the sqrt(N) dependence of collective Rabi frequency of single-atom excitation in the regime of Rydberg blockade. The interference of Rabi oscillations with different frequencies occurs due to the random loading of optical dipole traps or optical lattices. We have studied the effects of finite interaction strengths and finite laser line width on the visibility of the revivals. An experimental observation of this effect can be used as a signature of perfect Rydberg blockade without the need to measure the actual number of detected Rydberg atoms.

Förster resonance and dipole blockade in mesoscopic ensembles of cold Rb atoms

Observation of the relatively narrow three-photon resonance allowed us to start the experiments on studying the dipole blockade effect at laser excitation of an ensemble of the interacting Rb Rydberg atoms in the 37P state. Collective interactions between a few cold Rydberg atoms in a small laser excitation volume of 30-40 m in size were controlled using the Förster resonance Rb(37P)+Rb(37P) –>Rb(37S)+Rb(38S). The energy resonance is controlled by applying a weak dc electric field of 1.79 V/cm, thus switching the interactions between Rydberg atoms on and off. Switching the Förster resonance on did not change the spectrum of single-atom excitation (as there is no interaction for one atom), but it reduced the probabilities to excite more than one atom. The histograms of multi-atom signals also demonstrated the changes in detection statistics and reduction of the number of multi-atom events for the interacting Rydberg atoms. This evidences an observation of the partial dipole blockade effect. We have also conducted the experiments on a more detailed study of the electrically controlled Förster resonance Rb(37P)+Rb(37P) –>Rb(37S)+Rb(38S) at three-photon excitation by cw lasers using Stark switching of Rydberg levels. The resonance line shape has been found to be strongly dependent on the shape of electrical pulses used for switching.

Blockade of dipole matrix elements due to Förster resonance.

Radiative and collisional constants of excited atoms depend on the matrix elements of the dipole transitions and when they are blocked one can expect occurring a number of interesting phenomena in radiation-collisional kinetics. This may refer the both ultracold and normal media. Recent astrophysical studies of IR emission spectra registered from atmospheres of celestial objects revealed a gap in the radiation emitted by Rydberg atoms (RA) with the principal quantum number n values located around 10. Under the presence of external electric fields a rearrangement of RA emission spectra can be associated with the Förster resonance. The latter dramatically reduces the dipole matrix element between all optical transitions with \Delta n >1. Numerical simulations show, for instance, that small variations in Förster resonance detuning strongly affect the radiative rate constants of alkali atoms states in the vicinity of the Förster resonance resulting in an order of magnitude reduction of the intensity in some absorption lines. Other processes having the direct relation to the matrix elements refer the effects of dynamic chaos via collisional ionization. The Förster resonance detuning allows us to manipulate the random walk of the Rydberg electron in the manifold of quantum levels and hence change the excitation energies of RA, which lead to the anomalies in the IR spectra and in ionization constants. This work has been published in Advances in Space Research.

RF-assisted Forster resonances to enhance interactions between Rydberg atoms

Long-range interactions between cold Rydberg atoms are being investigated for neutral-atom quantum computing, quantum simulations, phase transitions in cold Rydberg gases and other important applications. These applications often require fine tuning of the interaction strength. It can be implemented using Förster resonances between Rydberg atoms controlled by a dc, microwave or radiofrequency (rf) electric field. We have observed and studied experimentally the highly resolved rf-assisted Förster resonances between 2-5 cold Rb Rydberg atoms. They correspond to an efficient transition from the van der Waals to dipole-dipole interactions due to Floquet sidebands of Rydberg levels appearing in the rf-field. Experiments were performed with cold 85Rb atoms in a magneto-optical trap. The rf-field of appropriate frequency and amplitude induced single- and multiphoton rf-transitions between collective states of a Rydberg quasimolecule formed by the interacting Rydberg atoms. We have shown that in the presence of the dc electric field they can be induced both for the ”accessible” Förster resonances which can be tuned by the dc field and for those which cannot be tuned and are ”inaccessible”. The van der Waals interaction of almost arbitrary high Rydberg states can thus be efficiently converted to resonant dipole-dipole interaction using the rf-field with frequencies below 1 GHz.

Counterintuitive principal quantum number dependence in the Auger-type ionization of Rydberg gases

Cold gases of atoms in Rydberg are prone to spontaneous ionization, and it is therefore important to understand how the ionization depends on the chosen principal quantum number n. We considered coupling between two ultraocold hydrogen Rydberg atoms using the model of dipole-dipole interaction, assuming that ionization occurs in an Auger type process, which presumes that one atom undergoes a transition n1- n1’ to a lower state, while the other atom uses the released energy to undergo a transition to the continuum n2-p2’. Using a simple asymptotic expression of the autoionization width [Eur. Phys. J. D 53, 329 (2009)] for the above process, we have demonstrated an interesting counterintuitive phenomenon: an essential increase (by n1 times) of the ionization efficiency is observed as the principal quantum number with the initial value n1 of the Rydberg atom decreases (i.e., increase ionization with decreasing size of one atom). It was shown that there exists an optimal relation between the quantum numbers n1 and n2, and was demonstrated numerically that such optimal atomic pair can make an essential contribution to the evolution of a cold Rydberg gas into a cold plasma. These results are being summarized in a manuscript for submission to Phys. Rev. Lett. On the more technical side, these studies have led to the formulation of a new calculation method for the evolution of Rydberg electron momentum and trajectories by combining the split propagation and Floquet techniques [Opt. Spectrosc. (2014)] .

Ultracold Rydberg atoms

Teams: Novosibirsk, St. Petersburg, Riga

Researchers involved

Key ER and ESR staff of Novosibirsk, St. Petersburg and Riga teams. In course of the project new PhD students join the teams.

Scientific highlights of Ultracold Rydberg atoms

We have developed novel theoretical schemes to perform quantum logic gates with mesoscopic atom ensembles which are suitable to implement one-way quantum computation. A quantum register can be represented by a two-dimensional array of optical dipole traps where each site is loaded by random number of atoms. Single- and two-qubit gates are performed using the developed by us earlier method of deterministic excitation of single Rydberg atoms and the newly developed method to compensate for the geometric phase incursion of the collective wave function. Dipole blockade is used for encoding the quantum information in the collective states of atom ensembles and for implementing two-qubit gates. Observation of the relatively narrow three-photon resonance allowed us to start the experiments on studying the dipole blockade effect at laser excitation of an ensemble of the interacting Rb Rydberg atoms in the 37P state when Forster resonance was switched on and off. Partial dipole blockade due to collective interactions between Rydberg atoms has been observed. Furthermore, Auger-type ionization in Rydberg gases has been studied and understanding about the dependence of this process on the principal quantum number has been gained. In this process, one atom Rydberg atom undergoes a transition to a lower state, while the other atom uses the released energy to undergo a transition to the continuum.

We have also shown theoretically that strongly interacting mesoscopic Rydberg ensembles with random and unknown number of atoms, which are coupled to a classical electromagnetic field, display the Jaynes-Cummings-type dynamics of single-atom laser excitation. The collapses and revivals of collective Rabi oscillations between Dicke states of the atomic ensemble result from the sqrt(N) dependence of collective Rabi frequency of single-atom excitation in the regime of Rydberg blockade. The interference of Rabi oscillations with different frequencies occurs due to the random loading of optical dipole traps or optical lattices. We have studied the effects of finite interaction strengths and finite laser line width on the visibility of the revivals. An experimental observation of this effect can be used as a signature of perfect Rydberg blockade without the need to measure the actual number of detected Rydberg atoms.

Ionization of Rydberg atoms in presence of a Förster resonance

Numerical study of the diffusion ionization of Rydberg atoms has been performed jointly by St. Petersburg and Novosibirsk teams. The ionization is induced by randomization of the trajectory of Rydberg electrons due to interaction with an electric microwave field. A model for ionization in the regime of dynamic chaos during a single atom–atom collision was proposed. Furthermore, a new method for controlling the chaotic regime in collision complexes was proposed which is based on the possibility of blocking optical transitions upon occurrence of Förster resonance under the conditions two-photon Stark resonance. This influences the dipole moment matrix elements and is similar to the phenomenon of Cooper minimum in the discrete energy range. The decay of the Rydberg complex induced by an external electromagnetic field turns out to be dependent on the preparation method.

Upon variation of the conditions, the reaction cross sections can increase by 2–3 orders of magnitude. The obtained results are extremely useful for solving the general problem of laser control of elementary atom-molecule processes with respect to changing the reaction rate, which is one of the fundamental problems of modern chemical physics. The results are published in [Russian J. Phys. Chem. B 5, 537 (2011)].

Novel aspects of three photon excitation of Rydberg states

A novel laser excitation technique eliminating the effects of recoil and Doppler broadening has been proposed by the Novosibirsk team. It is based on three-photon laser excitation of Rydberg states by three different laser beams arranged in a star-like geometry. It was demonstrated theoretically on the example of the 5S¹⁄₂ → 5P³⁄₂ → 6S¹⁄₂ → nP excitation in Rb atoms that, compared to the conventional one- and two-photon laser excitation, this approach provides a much narrower linewidth and longer coherence time for both cold atom samples and hot vapours, if the intermediate one-photon resonances of the three-photon transition are detuned by more than respective single-photon Doppler widths. The new excitation scheme is suitable for excitation of nP Rydberg states, which exhibit Stark-tuned Förster resonances at n ~38 for quantum information processing based on resonant dipole-dipole interaction of Rydberg atoms. Other Rydberg states can also be excited in the weak dc electric field due to wavefunction mixing and breakdown of the selection rules. The new technique is particularly attractive for recoil-free Rydberg excitation in Bose-Einstein condensates, which otherwise are notably heated by one- or two-photon absorption. The results are published in [Phys. Rev. A 84, 053409 (2011)].

Quantum computation using Rydberg blockade in an atomic ensemble

A new application of the adiabatic passage technique under the conditions of full Rydberg blockade has been proposed by Novosibirsk team to overcome the dependence of the laser exciting pulse parameters on the number of interacting atoms. It was found that a deterministic excitation of a single Rydberg atom can be implemented with high efficiency using the excitation by a linearly chirped laser pulse or by the stimulated Raman adiabatic passage (STIRAP) in mesoscopic ensembles with unknown number of atoms. These methods with removing ground-state atoms by an additional laser pulse allow for high-fidelity single-atom loading in optical dipole traps. A review of the state-of-the-art on application of neutral atoms as qubits of a quantum computer and use of single photons for information transfer has been provided in a recent review [Herald of the Russian Academy of Sciences (2013) in press], identifying the most promising directions of forthcoming research.

Effect of Photoions on Förster Resonances and Microwave Transitions in Cold Rydberg gases

Förster resonance lines Rb(37P) +Rb(37P) → Rb(37S) + Rb(38S) and microwave transitions nP → n’S, n’D between Rydberg states of cold Rb atoms in a magneto-optical trap (MOT) where studied jointly by Novosibirsk and St. Petersburg teams. The spectra exhibit a linewidth of 2–3 MHz irrespective of the interaction time between atoms or between atoms and microwave radiation, although one would expect the limit of the resonance width to be determined by the inverse of interaction time. The main source of line broadening was shown to be the inhomogeneous electric field of cold photoions that are generated under the excitation of the nP Rydberg states by the laser pulse. Due to the Stark effect, the presence of cold photoions leads to the deviation of the frequency of atomic transitions during the interaction time, thus leading to asymmetric broadening of a Förster resonance lines and microwave resonances. The application of an additional electric field pulse that rapidly extracts photoions produced by a laser pulse leads to a considerable narrowing of the microwave resonances lines and the Förster resonance. The analysis shows that the asymmetric broadening can be used out to nondestructively measure the mean field of ultracold plasma in a gas of cold Rydberg atoms. Moreover, our method for detecting charged particles makes it possible to measure the number of photoions generated in every laser pulse. The results have been published in [JETP 114, 14 (2012)].

Magnetic field induced transparency

Teams: Riga, Hsicnhu, Vilnius

Researchers involved

Key ER and ESR staff of Riga, Vilnius and Hsinchu teams. In course of the project new PhD students join the teams.

Scientific highlights of Magnetic field induced transparency

New insights into coherent and incoherent magneto-optical effects

Exact profiles of zero-field magneto-optical resonances depend on a number of parameters affecting several physical effects. Theoretical decomposition of these effects has been made by Riga team. A particular hyperfine transition (F”=2–>F’=3) of the D2 line of Rubidium-87 was chosen as the physical system. Zero field magneto-optical resonances with medium-range magnetic field amplitudes (up to several tens of Gauss) were recorded experimentally and described by the theoretical model to prove the ability of the model to describe experimental results. Further the model was altered by “turning on or off” several physical effects: destruction of coherences by the magnetic field in the ground and/or excited state and magnetic scanning of the magnetic sublevels of the atomic hyperfine levels with respect to the central frequency of the exciting laser radiation. Thus the features observable in the profile of magneto-optical resonance were attributed to some of the effects described in the theoretical model. It was confirmed that the narrow features observed in the vicinity of zero magnetic field are caused by coherent effects in the ground state of the atomic system while somewhat wider features (B~10G) are caused by the magnetic scanning within the split hyperfine structures within the Doppler broadened absorption profile of the chosen atomic line. The results are published in [J. Phys. B, 46, 185003 (2013)].

Magnetic field measurement using extremely thin cells.

Extremely thin cells (ETCs) with spacing between the inner glass walls in the range of 10^2 nm and containing alkali gases have been utilized as a demonstrator for magnetic field measurement. Magneto-optical resonances have been successfully described by a new model that takes into account relaxation due to atom collisions with the walls and takes into account the intensity distribution in the laser beam. The developed prototype magnetic field measurement device allows the measurement of magnetic fields and their gradients with high spatial resolution. The demonstration showed the measurements of Magneto-optical signals from an ETC mounted on a movable platform and controlled with submicron position resolution. Customized software was developed to perform the calibration and field gradient measurements, and sensitivity of 2 mG/nm was achieved. The results have been published in Phys. Rev. A, and a further manuscript is in preparation for a national technical journal.