Dark-state Polaritons Research Articles

Slow light in inhomogeneous and transverse fields

For all known massive particles, the value of the magnetic dipole moment is different from zero. In contrast, photons in vacuum have no magnetic moment. Here, we describe experimental studies that show that light, when transmitted through a dense atomic medium under the conditions of electromagnetically induced transparency (EIT), can behave as if it has acquired a magnetic dipole moment. In the area of solid-state physics, such effective particle properties (e.g. effective masses) are well known. In our experiments, slow light passing through a rubidium gas cell is deflected when exposed to a magnetic field gradient. The beam deflection is proportional to the propagation time through the cell and can be understood by assuming that dark-state polaritons have a nonzero effective magnetic moment aligned collinearly to the optical propagation axis. In more recent experiments, we have studied different dark-state configurations. We observe EIT, slow group velocities and stored light in a transverse magnetic field configuration, where the moving magnetic dipole is directed orthogonal to the optical propagation axis. The latter can be used for further studies of the quasiparticle properties of dark-state polaritons.

Dark-state polaritons in single- and double-Λmedia

We derive the properties of polaritons in single-$\ensuremath{\Lambda}$ and double-$\ensuremath{\Lambda}$ media using a microscopic equation-of-motion technique. In each case, the polaritonic dispersion relation and composition arise from a matrix eigenvalue problem for arbitrary control field strengths. We show that the double-$\ensuremath{\Lambda}$ medium can be used to up- or down-convert single photons while preserving quantum coherence. The existence of a dark-state polariton protects this single-photon four-wave mixing effect against incoherent decay of the excited atomic states. The efficiency of this conversion is limited mainly by the sample size and the lifetime of the metastable state.

A Stern–Gerlach experiment for slow light

Electromagnetically induced transparency allows for light transmission through dense atomic media by means of quantum interference. Media exhibiting electromagnetically induced transparency have very interesting properties, such as extremely slow group velocities. Associated with the slow light propagation are quasiparticles, the so-called dark polaritons, which are mixtures of a photonic and an atomic contribution. We here demonstrate that these excitations behave as particles with a nonzero magnetic moment, which is in clear contrast to the properties of a free photon. It is found that light passing through a rubidium gas cell under the conditions of electromagnetically induced transparency is deflected by a small magnetic field gradient. The deflection angle is proportional to the optical propagation time through the cell. The observed beam deflection can be understood by assuming that dark state polaritons have an effective magnetic moment. Our experiment can be described in terms of a Stern-Gerlach experiment for the polaritons.

Dark-state polaritons for quantum memory in a five-levelM-type atomic ensemble

Dark-state polaritons in a five-level $M$-type atomic ensemble are proposed in the electromagnetically induced transparency. Under conditions of the low excitation limit and adiabatic following, the quantum field can be mapped onto the atomic polarization states, forming the shape preserving quantum states of polaritons. Two channels for robust quantum memory are provided, which enables the potential applications in quantum-information processing.

Theory of dark-state polariton collapses and revivals

We investigate the dynamics of dark-state polaritons in an atomic ensemble with ground-state degeneracy. A signal light pulse may be stored and retrieved from the atomic sample by adiabatic variation of the amplitude of a control field. During the storage process, a magnetic field causes rotation of the atomic hyperfine coherences, leading to collapses and revivals of the dark-state polariton number. These collapses and revivals should be observable in measurements of the retrieved signal field, as a function of storage time and magnetic field orientation.

Observation of Dark State Polariton Collapses and Revivals

By time-dependent variation of a control field, both coherent and single-photon states of light are stored in, and retrieved from, a cold atomic gas. The efficiency of retrieval is studied as a function of the storage time in an applied magnetic field. A series of collapses and revivals is observed, in very good agreement with theoretical predictions. The observations are interpreted in terms of the time evolution of the collective excitation of atomic spin wave and light wave, known as the dark-state polariton.

Raman adiabatic transfer of optical states in multilevel atoms

We analyze electromagnetically induced transparency and light storage in an ensemble of atoms with multiple excited levels (multi-Lambda configuration) which are coupled to one of the ground states by quantized signal fields and to the other one via classical control fields. We present a basis transformation of atomic and optical states which reduces the analysis of the system to that of EIT in a regular 3-level configuration. We demonstrate the existence of dark state polaritons and propose a protocol to transfer quantum information from one optical mode to another by an adiabatic control of the control fields.

Storage and retrieval of single photons transmitted between remote quantum memories

An elementary quantum network operation involves storing a qubit state in an atomic quantum memory node, and then retrieving and transporting the information through a single photon excitation to a remote quantum memory node for further storage or analysis. Implementations of quantum network operations are thus conditioned on the ability to realize matter-to-light and/or light-to-matter quantum state mappings. Here we report the generation, transmission, storage and retrieval of single quanta using two remote atomic ensembles. A single photon is generated from a cold atomic ensemble at one site , and is directed to another site through 100 metres of optical fibre. The photon is then converted into a single collective atomic excitation using a dark-state polariton approach. After a programmable storage time, the atomic excitation is converted back into a single photon. This is demonstrated experimentally, for a storage time of 0.5 microseconds, by measurement of an anti-correlation parameter. Storage times exceeding ten microseconds are observed by intensity cross-correlation measurements. This storage period is two orders of magnitude longer than the time required to achieve conversion between photonic and atomic quanta. The controlled transfer of single quanta between remote quantum memories constitutes an important step towards distributed quantum networks.

Polariton picture of light propagation and storing in a tripod system

Light propagation and storing in a medium of atoms in the tripod configuration, driven by two control pulses are investigated. General situations are studied in which the releasing control pulses need not be replicas of those used at the storage stage and/or additional manipulations have been performed on a pair of atomic coherences, in which the pulse had been written. To completely describe the process we generalize the polariton description by modifying the concept of the dark-state polariton and by introducing a second polariton. The latter is a combination of two atomic coherences and gives account of a part of the signal field which remains trapped inside the medium after the release stage. We show how external manipulations at the storage stage can be taken into account in the polariton analysis and present some formulae which predict the shapes of the released and trapped parts of the pulse.

Decoherence in collective quantum memories for photons

The influence of decoherence on quantum memories for photons based on atomic ensembles is discussed. It is shown that despite the large entanglement of the collective storage states, corresponding to single photons or nonclassical states of light, the sensitivity to decoherence does not scale with the number of atoms. This is due to the existence of equivalence classes of storage states, which have the same projection onto the relevant quasiparticle mode (dark-state polariton). Several decoherence processes resulting from uncorrelated individual reservoir couplings are analyzed in detail: single-atom spin flips and dephasing, atom loss, and motion of atoms. Furthermore, it is shown that the sensitivity to collective decoherence processes that affect all polariton modes with comparable strength does also not increase with the number of atoms.

The dark-state polaritons of a double-Λ atomic ensemble

We study the interaction of two quantized fields with a double-Λ system driven by two classical control fields with variable complex Rabi frequencies. There exists one normal mode of the quantum fields that propagates without absorption. In the two-mode case of dark-state polaritons, we discuss the possibility of storing and retrieving the quantum state in this normal mode. This system can be also used to generate entangled state and, furthermore, it can act as a controllable beam splitter.

Dark-state polaritons using spontaneously generated coherence

A three-level atomic system in V-configuration (interacting with a single mode laser field) with parallel transition dipole moments exhibiting spontaneously generated coherence due to quantum interference of decaying channels is considered here for the purpose of storing light pulses. This system is equivalent to (with some restrictions) another three-level system in which ground state is coupled with one of the upper states but the upper states are coupled through a DC field and hence can be used to store electromagnetic pulse using the concept of dark-state-polariton.

Generalized dark-state polaritons for photon memory in multilevel atomic media

We generalize the concept of dark-state polariton in multilevel electromagnetically induced transparency systems. We show that the quantum states of light for the pulses can be mapped onto more than one collective atomic polarization states of the multilevel atomic system, which can act as a quantum state copier or divider. Such dark-state polaritons potentially have applications in quantum information processing.

Solitons formed by dark-state polaritons in an electromagnetic induced transparency

We show the possible stable soliton generation for the dark-state polaritons in an electromagnetically induced transparency medium composed of $\ensuremath{\Lambda}$-type atoms. Whether the solitons are dark or bright can be controlled by the coupling field intensity and the one-photon detuning of the probe field. The velocity, spatial, and time widths of the solitons can also be adjusted by the coupling light.

Quantum memory based on $\mathsf{\Lambda}$-atoms ensemble with two-photon resonance EIT

We study the $\Lambda$-atoms ensemble based quantum memory for the storage of the quantum information carried by a probe light field. Two atomic Rabi transitions of the ensemble are coupled to the quantum probe field and classical control field respectively with a same detuning. Making use of the hidden symmetry analysis developed recently for the on-resonance EIT case (Sun, Li, and Liu, Phys. Rev. Lett. 91, 147903 (2003)), we show that the dark states and dark-state polaritons can still exist for the case of two-photon resonance EIT. Starting from these dark states we construct a complete class of eigen-states of the total system. A explicit form of the adiabatic condition is also given in order to achieve the memory and retrieve of quantum information.

Scattering of dark-state polaritons in optical lattices and quantum phase gate for photons

We discuss the quasi one-dimensional (1-D) scattering of two counterpropagating, dark-state polaritons (DSPs), each containing a single excitation. DSPs are formed from photons in media with electromagnetically induced transparency and are associated with ultraslow group velocities. State-dependent elastic collisions of atoms at the same lattice site lead to a nonlinear interaction. It is shown that the scattering process in a deep optical lattice filled by cold atoms generates a large and homogeneous conditional phase shift between two individual polaritons. The latter has potential applications for a photonic phase gate. The quasi-1-D scattering problem is solved analytically and the influence of degrading processes such as dephasing due to collisions with ground-state atoms is discussed.

Coherent Atom Interactions Mediated by Dark-State Polaritons

We suggest a technique to induce effective, controllable interactions between atoms that is based on Raman scattering into an optical mode propagating with a slow group velocity. The resulting excitation corresponds to the creation of spin-flipped atomic pairs in a way that is analogous to correlated photon emission in optical parametric amplification. The technique can be used for fast generation of entangled atomic ensembles, spin squeezing, and applications in quantum information processing.

Quantum memory for photons: Dark-state polaritons

An ideal and reversible transfer technique for the quantum state between light and metastable collective states of matter is presented and analyzed in detail. The method is based on the control of photon propagation in coherently driven 3-level atomic media, in which the group velocity is adiabatically reduced to zero. Form-stable coupled excitations of light and matter (``dark-state polaritons'') associated with the propagation of quantum fields in Electromagnetically Induced Transparency are identified, their basic properties discussed and their application for quantum memories for light analyzed.

Dark-State Polaritons in Electromagnetically Induced Transparency

We identify form-stable coupled excitations of light and matter ("dark-state polaritons") associated with the propagation of quantum fields in electromagnetically induced transparency. The properties of dark-state polaritons such as the group velocity are determined by the mixing angle between light and matter components and can be controlled by an external coherent field as the pulse propagates. In particular, light pulses can be decelerated and "trapped" in which case their shape and quantum state are mapped onto metastable collective states of matter. Possible applications of this reversible coherent-control technique are discussed.