We present a detailed theoretical description of the generation of stationary light pulses by standing wave electromagnetically induced transparency in media comprised of stationary atoms. We show that, contrary to thermal gas media, the achievable storage times are limited only by the ground state dephasing rate of the atoms, making such media ideally suited for nonlinear optical interactions between stored pulses. Furthermore, we find significant quantitative and qualitative differences between the two types of media, which are important for quantum information processing schemes involving stationary light pulses.
We study a single two-level atom interacting with a reservoir of modes defined by a reservoir structure function with a frequency gap. Using the pseudomodes technique, we derive the main features of a trapping state formed in the weak coupling regime. Utilising different entanglement measures we show that strong correlations and entanglement between the atom and the modes are in existence when this state is formed. Furthermore, an unexpected feature for the reservoir is revealed. In the long time limit and for weak coupling the reservoir spectrum is not constant in time.
The stationary light pulse (SLP) refers to a zero-group-velocity optical pulse in an atomic ensemble prepared by two counter-propagating driving fields. Despite the uniqueness of an optical pulse trapped within an atomic medium without a cavity, observations of SLP so far have been limited to trapping a single optical pulse due to the stringent SLP phase-matching condition, and this has severely hindered the development of SLP-based applications. In this paper, we first show theoretically that the SLP process in fact supports two phase-matching conditions and we then utilize the result to expe…
We present theoretical and experimental results of coherent population trapping spectra on a multi-level $^{40}$Ca$^+$-type configuration, adding a third beam to the standard two-laser $Λ$ system to avoid undesired optical pumping. We show that the extra laser can preserve the nature of the dark resonances or introduce decoherence depending on its power. Experiments are carried out using a single trapped $^{40}$Ca$^+$ ion in the $S_{1/2}-P_{1/2}-D_{3/2}$ manifold. Theoretically, the problem is solved with a Floquet-like expansion of the Liouvillian that correctly predicts all of the measured s…
Efficient photon-photon interaction is one of the key elements for realizing quantum information processing. The interaction, however, must often be mediated through an atomic medium due to the bosonic nature of photons, and the interaction time, which is critically linked to the efficiency, depends on the properties of the atom-photon interaction. While the electromagnetically induced transparency effect does offer the possibility of photonic quantum memory, it does not enhance the interaction time as it fully maps the photonic state to an atomic state. The stationary light pulse (SLP) effect…
A 2-level atom with degenerate ground state interacting with a quantum field is investigated. We show, that the field drives the state of the atom to a stationary state, which is non-unique, but depends on the initial state of the system through some conserved quantities. This non-uniqueness follows from the degeneracy of the ground state of the atom, and when the ground subspace is two-dimensional, the family of stationary states will depend on a one-dimensional parameter. Only one of the stationary states in this family is a pure state, and this state coincides with the known non-coupled pop…
We demonstrate an atom localization scheme based on monitoring of the atomic coherences. We consider atomic transitions in a Lambda configuration where the control field is a standing wave field. The probe field and the control field produce coherence between the two ground states. We show that this coherence has the same fringe pattern as produced by a Fabry-Perot interferometer and thus measurement of the atomic coherence would localize the atom. Interestingly enough the role of the cavity finesse is played by the ratio of the intensities of the pump and probe. This is in fact the reason for…
The dynamics of two two-level dipole-dipole interacting atoms coupled to a common electromagnetic bath and closely located inside a lossy cavity, is reported. Initially injecting only one excitation in the two atoms-cavity system, loss mechanisms asymptotically drive the matter sample toward a stationary maximally entangled state. The role played by the closeness of the two atoms with respect to such a cooperative behaviour is carefully discussed. Stationary radiation trapping effects are found and transparently interpreted.
We propose the dynamic control of two-color stationary light in a double-lambda four-level system using electromagnetically induced transparency. We demonstrate the complete localization of two-color quantum fields inside a medium using coherence moving gratings resulting from slow-light based atom-field interactions in backward nondegenerate four-wave mixing processes. The quantum coherent control of the two-color stationary light opens a door to deterministic quantum information science which needs a quantum nondemolition measurement, where the two-color stationary light scheme would greatly…
The stationary solutions of the Gross-Pitaevskii equation can be divided in two classes: those which reduce, in the limit of vanishing nonlinearity, to the eigenfunctions of the associated Schrödinger equation and those which do not have linear counterpart. Analytical and numerical results support an existence condition for the solutions of the first class in terms of the ratio between their proper frequency and the corresponding linear eigenvalue. For one-dimensional confined systems, we show that solutions without linear counterpart do exist in presence of a multi-well external potential. Th…
Inhomogeneous broadening of energy levels is one of the principal limiting factors for achieving "slow" or "stationary" light in solid state media by means of electromagnetically induced transparency (EIT), a quantum version of stimulated Raman adiabatic passage (STIRAP). Stark-shift-chirped rapid-adiabatic-passage (SCRAP) has been shown to be far less sensitive to inhomogeneous broadening than STIRAP, a population transfer technique to which it is closely related. We further optimise the pulses used in SCRAP to be even less sensitive to inhomogeneous broadening in a lambda-type three-level sy…
We discuss stationary light created by a pair of counter-propagating control fields in Lambda-type atomic gases with electromagnetically induced transparency for the case of negligible Doppler broadening. In this case the secular approximation used in the discussion of stationary light in hot vapors is no longer valid. We discuss the quality of the effective light-trapping system and show that in contrast to previous claims it is finite even for vanishing ground-state dephasing. The dynamics of the photon loss is in general non exponential and can be faster or slower than in hot gases.
Spatial and temporal evolution is studied of two powerful short laser pulses having different wavelengths and interacting with a dense three-level Lambda-type optical medium under coherent population trapping. A general case of unequal oscillator strengths of the transitions is considered. Durations of the probe pulse and the coupling pulse $T_{1,2}$ ($T_2>T_1$) are assumed to be shorter than any of the relevant atomic relaxation times. We propose analytical and numerical solutions of a self-consistent set of coupled Schrödinger equations and reduced wave equations in the adiabatic limit with …
We consider the properties of stationary states and the dynamics of Bose-Einstein condensates (BECs) in a double-well (DW) potential with pair tunneling by using a full quantum-mechanical treatment. Furthermore, we study the quantum quench dynamics of the DW system subjected to a sudden change of the Peierls phase. It is shown that strong pair tunneling evidently influences the energy spectrum structure of the stationary states. For relatively weak repulsive interatomic interactions, the dynamics of the DW system with a maximal initial population difference evolves from Josephson oscillations …
We present a general scheme to determine the loss-free adiabatic eigensolutions (dark-state polaritons) of the interaction of multiple probe laser beams with a coherently driven atomic ensemble under conditions of electromagnetically induced transparency. To this end we generalize the Morris-Shore transformation to linearized Heisenberg-Langevin equations describing the coupled light-matter system in the weak excitation limit. For the simple lambda-type coupling scheme the generalized Morris-Shore transformation reproduces the dark-state polariton solutions of slow light. Here we treat a close…
The wave function of a moderately cold atom in a stationary near-resonant standing light wave delocalizes very fast due to wave packet splitting. However, we show that frequency modulation of the field may suppress packet splitting for some atoms having specific velocities in a narrow range. These atoms remain localized in a small space for a long time. We propose that in a real experiment with cold atomic gas this effect may decrease the velocity distribution of atoms (the field traps the atoms with such specific velocities while all other atoms leave the field)
We have studied stationary and quasi-stationary signal light pulses in cold lambda-type atomic media driven by counterpropagating control laser fields at the condition of electromagnetically induced transparency. By deriving a dispersion relation we present spectral and temporal properties of the signal light pulse and a significant influence of atomic decoherence on the coupled stationary light pulses for spatial splitting. Finally we discuss quasi-stationary light pulse evolution characterized by frozen spatial spreading for a robust coherent control of slow light pulses.
We present and analyze a novel concept for blue-detuned evanescent field surface traps for cold neutral atoms based on two-mode interference in ultra-thin optical fibres. When two or more transverse modes with the same frequency co-propagate in the fibre, their different phase velocities cause a stationary interference pattern to establish. Intensity minima of the evanescent field at any distance from the fibre surface can be created and an array of optical microtraps can thus be obtained in the evanescent field. We discuss three possible combinations of the lowest order modes, yielding traps …
We give numerical estimates of various unstable stationary solutions of the Gross--Pitaevskii equation in an axially symmetric set up with a linear trapping potential along the symmetry axis, and a quadratic trapping along the radial direction. These represent topological coherent modes of Bose--Einstein condensates in a gravito optical surface trap (GOST). Despite their instability, we find that many of these solutions decay sufficiently slow, so that they could be realized experimentally.
We propose a practical physical system for creation of a stationary entanglement by dissipation without employing the environment engineering techniques. The system proposed is composed of two perfectly distinguishable atoms, through their significantly different transition frequencies, with only one atom addressed by an external laser field. We show that the arrangement would easily be realized in practice by trapping the atoms at the distance equal to the quarter-wavelength of a standing-wave laser field and locating one of the atoms at a node and the other at the successive antinode of the …
We propose and analyze a mechanism for Bose-Einstein condensation of stationary dark-state polaritons. Dark-state polaritons (DSPs) are formed in the interaction of light with laser-driven 3-level Lambda-type atoms and are the basis of phenomena such as electromagnetically induced transparency (EIT), ultra-slow and stored light. They have long intrinsic lifetimes and in a stationary set-up with two counterpropagating control fields of equal intensity have a 3D quadratic dispersion profile with variable effective mass. Since DSPs are bosons they can undergo a Bose-Einstein condensation at a cri…
We analyze the ac Stark shift of a cesium atom interacting with far-off-resonance guided light fields in the nanofiber-based two-color optical dipole trap realized by Vetsch \textit{et al.} [Phys. Rev. Lett. \textbf{104}, 203603, (2010)]. Particular emphasis is given to the fictitious magnetic field produced by the vector polarizability of the atom in conjunction with the ellipticity of the polarization of the trapping fields. Taking into account the ac Stark shift, the atomic hyperfine interaction, and a magnetic interaction, we solve the stationary Schrödinger equation at a fixed point in sp…
One of the most well known relativistic field theory models is the Thirring model (TM). Its realization can demonstrate the famous prediction for the renormalization of mass due to interactions. However, experimental verification of the latter requires complex accelerator experiments whereas analytical solutions of the model can be extremely cumbersome to obtain. In this work, following Feynman's original proposal, we propose a alternative quantum system as a simulator of the TM dynamics. Here the relativistic particles are mimicked, counter-intuitively, by polarized photons in a quantum nonli…
