Velocity-selective Coherent Population Trapping Research Articles

Motion-selective coherent population trapping for subrecoil cooling of optically trapped atoms outside the Lamb-Dicke regime

We propose a scheme that combines velocity-selective coherent population trapping (CPT) and Raman sideband cooling (RSC) for subrecoil cooling of optically trapped atoms outside the Lamb-Dicke regime. This scheme is based on an inverted $\mathsf{Y}$ configuration in an alkali-metal atom. It consists of a $\mathrm{\ensuremath{\Lambda}}$ formed by two Raman transitions between the ground hyperfine levels and the $D$ transition, allowing RSC along two paths and formation of a CPT dark state. Using the state-dependent difference in vibration frequency of the atom in a circularly polarized trap, we can tune the $\mathrm{\ensuremath{\Lambda}}$ to make only the motional ground state a CPT dark state. We call this scheme motion-selective coherent population trapping (MSCPT). We write the master equations for RSC and MSCPT and solve them numerically for a $^{87}\mathrm{Rb}$ atom in a one-dimensional optical lattice when the Lamb-Dicke parameter is 1. Although MSCPT reaches the steady state slowly compared with RSC, the former consistently produces colder atoms than the latter. The numerical results also show that subrecoil cooling by MSCPT outside the Lamb-Dicke regime is possible under a favorable, yet experimentally feasible, condition. We explain this performance quantitatively by calculating the relative darkness of each motional state. Finally, we discuss the application of the MSCPT scheme to an optically trapped diatomic polar molecule whose Stark shift and vibration frequency exhibit large variations depending on the rotational quantum number.

Quantum treatment of laser cooling on weak transitions: multipeaks and bimodal momentum distributions

The work is devoted to the study of the features and parameters of the momentum distributions of atoms laser cooled on weak optical transitions. It was shown that atoms distributions are described by a bimodal momentum distribution whose characteristics depends on the parameters of the light field. In a strong field a velocity selective coherent population trapping effect is observed.

Uncondensed atoms in the regime of velocity-selective coherent population trapping

We consider the model of a Bose condensate in the regime of velocity-selective coherent population trapping. As a result of interaction between particles, some fraction of atoms is outside the condensate, remaining in the coherent trapping state. These atoms are involved in brief events of intense interaction with external resonant electromagnetic fields. Intense induced and spontaneous transitions are accompanied by the exchange of momenta between atoms and radiation, which is manifested as migration of atoms in the velocity space. The rate of such migration is calculated. A nonlinear kinetic equation for the many-particle statistical operator for uncondensed atoms is derived under the assumption that correlations of atoms with different momenta are insignificant. The structure of its steady-state solution leads to certain conclusions about the above-mentioned migration pattern taking the Bose statistics into consideration. With allowance for statistical effects, we derive nonlinear integral equations for frequencies controlling the migration. The results of numerical solution of these equations are represented in the weak interatomic interaction approximation.

Dissipative preparation of spatial order in Rydberg-dressed Bose-Einstein condensates.

We propose a technique for engineering momentum-dependent dissipation in Bose-Einstein condensates with nonlocal interactions. The scheme relies on the use of momentum-dependent dark states in close analogy to velocity-selective coherent population trapping. During the short-time dissipative dynamics, the system is driven into a particular finite-momentum phonon mode, which in real space corresponds to an ordered structure with nonlocal density-density correlations. Dissipation-induced ordering can be observed and studied in present-day experiments using cold atoms with dipole-dipole or off-resonant Rydberg interactions. Because of its dissipative nature, the ordering does not require artificial breaking of translational symmetry by an optical lattice or harmonic trap. This opens up a perspective of direct cooling of quantum gases into strongly interacting phases.

Coherent population trapping in aΛconfiguration coupled by magnetic dipole interactions

We report our study on coherent population trapping (CPT) in a $\ensuremath{\Lambda}$ configuration coupled by magnetic dipole interactions. The $\ensuremath{\Lambda}$ configuration is formed by bichromatic radio-frequency fields coupling a pair of Zeeman sublevels in one hyperfine level of an alkali-metal atom to another sublevel in the other hyperfine level. The Zeeman sublevel at the apex is coupled to a state in the $nP$ manifold via an optical transition on one of the spectroscopic $D$ lines to induce optical pumping to a dark state. The configuration is closed without leakage to other Zeeman sublevels. We use lithium atoms in an optical trap for our experimental study. The system allows independent control of the main parameters characterizing CPT, which include the upper-state decay rate and the decoherence rate as well as the Rabi frequencies. By turning off the applied fields, the system is frozen so that its quantum state can be measured precisely. We studied the line shapes and dynamics of the CPT system, and measured the phase relation of the dark superposition state to find excellent agreement with theory. The possible application of the scheme as a method to cool optically trapped atoms below the recoil limit in a manner analogous to velocity-selective coherent population trapping is discussed.

Interactions of condensate atoms in the process of velocity-selective coherent population trapping

The properties of a one-dimensional atomic Bose condensate are studied under the assumption that the condensation leads to a state of velocity-selective coherent population trapping. This state is characterized by the quantum correlation (entanglement) between the intrinsic angular momentum of an atom and its translational motion underlying nontrivial features of the condensate. The effects of weak interatomic interaction are taken into account. The steady state of above-condensate atoms corresponding to the slow decay of the state with coherent population trapping is found. The dynamic problem concerning the evolution of the system of above-condensate atoms after switching off the optical field forming the state with coherent population trapping is solved. The solution is found by the diagonalization of the Hamiltonian based on introducing the Bogoliubov quasiparticles with the unusual dispersion law.

Commentary: Controlling electromagnetic metamaterials

The last two decades have been witness to two exciting and independent developments that have forever changed our conventional view of how light interacts with matter. One relates to coherent control via quantum interference, wherein the possibility of making an otherwise opaque medium transparent [1], now known as electromagnetically induced transparency (EIT), set off intense research activity. EIT essentially requires careful creation of atomic coherence, that results in diverse effects varying from almost freezing light in its tracks (slow light) to freezing atoms to nanoKelvin temperatures via velocity-selective coherent population trapping. The second development relates to metamaterials whose origins are very classical in nature. In electromagnetics, these designer materials were originally proposed for realizing a super-lens wherein the evanescent field becomes the work horse that accords sub-wavelength resolution in imaging [2]. Since then a variety of metamaterials have been proposed, where even the propagating fields can be dramatically controlled, as in electromagnetic cloaks wherein the fields are maneuvered around an obstacle so as to make it invisible. The biggest technological contraints in realizing large-scale device applications of metamaterials have been two. The first is the large dissipation associated with an inherently resonant phenomenon. The second arises due to the very design of metamaterial; once the metamaterial structures (inclusions) are fabricated, they offer little maneuverability in terms of the operating frequency. However, both EIT and metamaterials have truly lifted the tedium associated with the usual classical linear phenomena involving light. It is commonly believed this is just the beginning of a long journey, where our inherent drive to control gainfully these and many other wondrous effects will be the prime mover of future developments. The marriage of these two diverse developments is highlighted here, with a word of caution: one can only naively guess the surprises this relationship will bring forth. In order to achieve a composite material combining the attributes of EIT and metamaterials, one simple design involves immersing the metamaterial in a dilute atomic gas whose frequency-selective absorption can be exploited to manipulate the metamaterial response [3]. Furthermore, a combination of light fields accords extra control over the metamaterial via the absorption and dispersion of the atomic gas through the atomic coherence (quantum) route, based on effects like EIT. The price of working at near-resonant conditions is the large dispersion with frequency accompanied by large loss. EIT-based control exploits the large frequency-dispersion and yet provides substantially decreased loss which is even lower than the metallic losses in a narrow-bandwidth regime. The large variation of the refractive index of the EIT medium results in the freezing of currents in the metallic inclusions of the metamaterial, thereby lowering loss. The most critical issues that govern this alliance arise from the very nature of the two partners. EIT is a quantum phenomenon, whereas metamaterials are described classically. Quantum phenomena are extremely susceptible to the surroundings, and using a solid or liquid medium severely restricts the performance of the quantum partner. For example, rareearth ions implanted in crystals have been shown to exhibit EIT only at extremely low temperatures where the phonon noise is sufficiently suppressed such that the ground-state

Increased trapping efficiency with force-assisted velocity-selective coherent population trapping

We study a class of laser cooling schemes that combine velocity-selective coherent population trapping (VSCPT) with Doppler cooling mechanisms. The Doppler mechanism prevents the atoms from diffusing into the region of high momentum, thereby removing the characteristic long-time asymptotic behaviour of VSCPT where, in the end, all the atoms escape from the trap. It is shown that the transition Jg = 2 to Je = 1 while maintaining the simple field configuration present in the original VSCPT case provides the additional Doppler mechanism and leads to virtually zero temperature without the loss of atoms that characterize the original VSCPT dynamics.

Detection of atomic entanglement and electromagnetically induced transparency in velocity-selective coherent population trapping

We investigate theoretically the optical properties of an atomic gas that has been cooled by the laser cooling method of velocity-selective coherent population trapping. We demonstrate that the application of a weak laser pulse gives rise to a backscattered pulse, which is a direct signal for the entanglement in the atomic system, and which leads to single-particle entanglement on the few-photon level. If the pulse is applied together with the pump lasers, it also displays the phenomenon of electromagnetically induced transparency. We suggest that the effect should be observable in a gas of rubidium atoms.

Sub-Doppler laser cooling on combined optical transitions

We study the laser cooling process in a complex lambda system in the presence of force-assisted bichromatic velocity-selective coherent population trapping. Our theoretical model includes atomic transitions based on two ground states, Fg=1 and Fg′=3, and one excited state, Fe=2, excited by a bichromatic laser field tuned in resonance with the Fg=1→Fe=2 and Fg′=3→Fe=2 transitions. The analyzed optical scheme may be useful for alternative transverse cooling in experiments with group III atoms (Al, Ga, In).

Evolution of coherent dark states

We present a set of exploratory experimental studies of velocity-selective coherent population trapping (VSCPT) on the $2{}^{3}{S}_{1}\ensuremath{\rightarrow}2{}^{3}{P}_{1}$ transition of Helium, including the effect of an external magnetic field along the propagation direction of the light. We also investigate in detail the effects of the laser detuning and the atom-laser interaction time in determining the shape and width of the VSCPT velocity distribution. Our data corroborates some previous theory and calculations. We demonstrate that the only observable effect of a magnetic field applied along the direction of light propagation is to shift the center of the VSCPT peaks in the atomic velocity distribution by an amount proportional to the magnitude of the applied field. We present a semiclassical picture that describes the atomic motion of VSCPT in such a B field.

Velocity-selective coherent population trapping of two-level atoms

We have demonstrated velocity-selective coherent population trapping (VSCPT) in a two-level system created by circularly polarized light driving the $2{}^{3}{S}_{1}\ensuremath{\rightarrow}3{}^{3}{P}_{2}$ transition in metastable helium. It is quite different from the usual VSCPT because there need be no consideration of selection rules, polarization, or internal atomic states. This most primitive case elicits the simple nature of VSCPT as a special kind of quantum interference, and demonstrates the presence of VSCPT in a system that has only two internal levels. It is readily observed for this transition because the ratio of the recoil frequency to the natural linewidth is 0.22, two orders of magnitude larger than for most laser cooling experiments. Our trapped state is fed by Doppler cooling, which is unusually effective here because of the large recoil, and is totally absent in previously described VSCPT experiments.

Entanglement between Atomic Internal and External States in Velocity-Selective Coherent Population Trapping

The nonfactorizable atomic wavefunctions prepared by the process of laser cooling based on velocity-selective coherent population trapping are analyzed. The entanglement of the atomic wavefunction is presented and discussed. The decoherence processes modifying the atomic entanglement are examined.

Entanglement between Atomic Internal and External States in Velocity-Selective Coherent Population Trapping

Entanglement between Atomic Internal and External States in Velocity-Selective Coherent Population Trapping

Experimental Investigation of Nonergodic Effects in Subrecoil Laser Cooling

We present the first detailed investigation of the line shape of the momentum distribution of atoms cooled far below the recoil limit. This distribution is deduced from a direct measurement of the atomic spatial correlation function of metastable helium atoms cooled by velocity-selective coherent population trapping. The measured line shape is then compared to the prediction of an analytical model of this cooling based on Levy statistics. A very good agreement is found between experiment and theory and fundamental features such as self-similarity and nonergodicity are identified.

How dark is a grey state?

We present experimental results showing that a dark state with finite lifetime, a grey state, becomes darker the more the atom is exposed to on-resonant light. We discuss this phenomenon theoretically in the context of the complex eigenenergies and show that it can be understood qualitatively in terms of the quantum Zeno effect. The predicted dependence of the lifetime on the composition of the grey state and on the light intensity is experimentally confirmed with caesium atoms. This has implications for velocity-selective coherent population trapping and adiabatic transfer.

Atom cooling by VSCPT: Accumulation plus filtering

We study laser cooling by velocity-selective coherent population trapping (VSCPT) in a double-Λ scheme with decay beyond the working levels. We show that this additional decay channel filters diffused atoms from trapped ones and provides an ultrasharp atomic momentum distribution.

Laser cooling of internal degrees of freedom of molecules by dynamically trapped states

In the last several years we have discovered a variety of remarkable pulse strategies for manipulating molecular motion by employing a design strategy we call “local optimization.'' Here we review the concept of local optimization and contrast it with optimal control theory. By way of background, we give highlights from two recent examples of the method: (1) a strategy for eliminating population transfer to one or many excited electronic states during strong field excitation, an effect we call ‘optical paralysis’; (2) a generalization of the counterintuitive STIRAP (stimulated Raman adiabatic passage) pulse sequence from three levels to N levels, a strategy we call ‘straddling STIRAP.' We then turn to a third example, which is the main subject of this paper: laser cooling of molecular internal degrees of freedom. We study a model that includes both coherent interaction with the radiation field and spontaneous emission; the latter is necessary to carry away the entropy from the molecule. An optimal control calculation was performed first and succeeded in producing vibrational cooling, but the resulting pulse sequence was difficult to interpret. Local optimization subsequently revealed the cooling mechanism: the instantaneous phase of the laser is locked to the phase of the transition dipole moment between the excited state amplitude and v=0 of the ground state. Thus, the molecules that reach v=0 by spontaneous emission become decoupled from the field, and no longer absorb, while molecules in all other states are continually repumped. The mechanism could be called “vibrationally selective coherent population trapping,'' in analogy to the corresponding mechanism of velocity selective coherent population trapping in atoms for sub-Doppler cooling of translations.

Exotic quantum dark states

We extend studies of velocity selective coherent population trapping to atoms having a J = 1! J = 0 transition. When placed in a two-dimensional laser eld these atoms are optically pumped into dierent velocity selective nonabsorbing states. Each of these distinct energy eigenstates exhibits a unique entanglement between its internal and external degrees of freedom. We use a graphical method that makes easier the description of these states. We conrm our predictions experimentally.

Several asymptotic cooling features in an arbitrary degenerate Λ system

The difference between excited and ground atomic-momentum distributions, in an arbitrary degenerate Λ-type atomic system interacting with two counterpropagating fields, is exploited to construct a set of analytical functions that have features similar to the long-time atomic-momentum distributions due to cooling by velocity-selective coherent population trapping [J. Opt. Soc. Am. B 6 (1989) 2112].