Quantum interface between light and atomic ensembles

During the past decade the interaction of light with multiatom ensembles has attracted much attention as a basic building block for quantum information processing and quantum state engineering. The field started with the realization that optically thick free space ensembles can be efficiently interfaced with quantum optical fields. By now the atomic ensemble-light interfaces have become a powerful alternative to the cavity-enhanced interaction of light with single atoms. Various mechanisms used for the quantum interface are discussed, including quantum nondemolition or Faraday interaction, quantum measurement and feedback, Raman interaction, photon echo, and electromagnetically induced transparency. This review provides a common theoretical frame for these processes, describes basic experimental techniques and media used for quantum interfaces, and reviews several key experiments on quantum memory for light, quantum entanglement between atomic ensembles and light, and quantum teleportation with atomic ensembles. The two types of quantum measurements which are most important for the interface are discussed: homodyne detection and photon counting. This review concludes with an outlook on the future of atomic ensembles as an enabling technology in quantum information processing.

Figure 1

(Color online) Elementary level schemes: (a) A simple absorption scheme with the quantum fields $a_{\pm }$ mapped onto the atomic states $a_A$. (b) Beam-splitter-type interaction—basis for Raman and EIT memory schemes. (c) Parametric-gain-type interaction—basis for entanglement schemes. (d) Quantum nondemolition (or Faraday) interaction—basis for entanglement, memory, and teleportation schemes.

Figure 2

(Color online) $\Lambda$ configuration with dominant population of level |0⟩: (a) Beam-splitter interaction with the quantum field of the single photon Rabi frequency $g$ on the $|0⟩\to |e⟩$ and the strong light with the Rabi frequency $\Omega$ on the $|e⟩\to |1⟩$ transition. The two fields are in two-photon resonance with a detuning $\Delta$ from the excited state $|e⟩$. Decay due to spontaneous emission goes back to one of the ground states at the rates ${\gamma }_{0\left(1\right)}$ or to other levels (not shown) summing up to a total rate $\gamma$. (b) Parametric-gain interaction. (c) Faraday interaction: Atoms are polarized to |0⟩, the strong field is linearly polarized along $x$ and drives the up transitions with the Rabi frequency $\Omega$, and the quantum field in $y$ polarization couples to the cross transitions with the single photon Rabi frequency $g$. The fields are in two photon resonance with a detuning $\Delta$ from the excited states. Decay due to spontaneous emission goes back to one of the ground states at the rates ${\gamma }_{x\left(y\right)}$ or to other levels (not shown) at the rate $\gamma$.

Figure 3

(Color online) Coefficients $a_0$, $a_1$, $a_2$ for, respectively, scalar, vector, and tensor polarizability vs detuning $\Delta$ of probe light driving the $6S_{1∕2}\to 6P_{3∕2}$ transition in ${}^{133}\mathrm{Cs}$. The inset shows the relevant levels and energy scales.

Figure 4

(Color online) A magnetic field along the axis of polarization causes Zeeman splitting ${\omega }_L$ of ground-state levels. Photons will be scattered from the classical light, driving the $\pi$ transitions, to the quantum field, coupling to the cross $\sigma$ transitions, at sideband frequencies ${\omega }_0\pm {\omega }_L$ from the carrier frequency ${\omega }_0$.

Figure 5

(Color online) Polarimetric measurement of light.

Figure 6

(Color online) Level scheme for Faraday interaction. (a) For the quantization axis along $x$: Atoms are polarized to ${|+⟩}_x$, laser light is linear polarized along $x$ and drives the up transitions, while the quantum field in $y$ polarization couples to the cross transitions. (b) The same interaction with the axis of quantization taken along $z$: Circular light components of equal intensity cause ac-Stark shifts of equally populated states ${|\pm ⟩}_z$.

Figure 7

(Color online) QND interaction for measurement of pseudospin composed of hyperfine ground states of Cs. (a) Level scheme for ${}^{133}\mathrm{Cs}$ with probe light tuned in between hyperfine levels $F=3,4$ of the $6^2{S}_{1∕2}$ ground state. (b) Differential phase shift $\Phi$ due to the $F=3\to F^{\prime }=2,3,4$ and the $F=4\to F^{\prime }=3,4,5$. At magic frequencies the phase shift vanishes.

Figure 8

(Color online) Paraffin coated cesium cell.

Figure 9

(Color online) Deterministic entanglement of two atomic ensembles via QND measurement. (a) Experimental setup. Dashed lines, optical pumping; solid arrow, entangling light direction. (b) Pulse sequence and the layout of the experiment. (1) optical pumping pulse, (2) entangling pulse, (3) verifying pulse. (c) Projection noise of atoms. (d) EPR variance of the entangled state normalized to the projection noise level, i.e., to the variance for a separable coherent state of two ensembles.

Figure 10

(Color online) DLCZ protocol. (a) Entanglement between light and atoms is generated by a parametric gain interaction in two distant ensembles. Detection of a photon by one of the two photodetectors after the optical beam splitter probabilistically generates entanglement between the two ensembles. (b) The atomic excitation in one-half of an entangled pair of atomic ensembles (dashed line) is read out onto light with the light-atom beam-splitter interaction and mixed on an optical beam splitter with its counterpart from another entangled pair of ensembles. Photodetection swaps the entanglement so that now the outmost ensembles become entangled.

Figure 11

(Color online) $\mathrm{QND}+\text{feedback}$ memory experimental setup and pulse sequence. The state of light is encoded by the EOM in the sidebands of the strong pulse $\sqrt{n\left(t\right)}$. Two cells serve as the quantum memory unit. The feedback pulse proportional to the photodetector signal is applied to the rf magnetic coils. Inset: (1) optical pumping, (2) input pulse, (3) feedback rf pulse, (4) rf pulse rotating atomic $P$ into $X$ used for half of verification pulses, (5) verifying pulse. From [128].

Figure 12

(Color online) Atomic coherent memory results. The mean values for both quadratures of the input light, atomic memory, and the output light are identical to within a chosen factor (here 0.8). From 128.

Figure 13

(Color online) Variance of the atomic memory state for input coherent states with $n⩽8$. The variance of $1∕2$ corresponds to the memory variance equal to the input light variance, that is, to a perfect memory. Above the $3∕2$ level is the classical memory performance for arbitrary coherent states. The dashed line is the best classical performance for the states within the $n⩽8$ class. Diamonds and squares are experimental results from 128.

Figure 14

(Color online) Protocols for state swapping. (a) Setup for two-pass protocol for read-out of atomic states as suggested by 150 and, with an additional magnetic field applied along $x$, for full state exchange or creation of entanglement between light and atoms as suggested by 180. (b) State swap between two ensembles coupled to a common cavity mode based on adiabatic passage as demonstrated by (219. The classical pulses ${\Omega }_i$ are applied in a counterintuitive sequence.

Figure 15

(Color online) EIT-based memory setup. (a) Level scheme and sequence of control pulses. Left, parametric interaction for a probabilistic generation of an excitation in the source ensemble; center and right, EIT-based beam-splitter interactions for storage and retrieval. (b) Setup showing the source ensemble of the nonclassical photon flux and the memory ensemble (target atoms). A count in detector S1 or S2 is a condition for starting the process. Detectors AS1 and AS2 analyze the statistics of the input and output memory photons. From 74.

Figure 16

(Color online) EIT-based memory. Probability of detecting a photon downstream the memory ensemble (left axis). The points around $\tau =0$, the moment when the input pulse is launched are due to the imperfect memory leading to the leakage of photons through it. The strong field (right axis) is turned off around $\tau =0$ and turned on again at $\tau =1\mu \sec$ leading to the retrieved pulses with the overall storage retrieval probability of 17%. From 50.

Figure 17

(Color online) Two memory ensembles store two components of an entangled state which are later retrieved and analyzed by two pairs of coincidence detectors $D_{1,2}$.

Figure 18

(Color online) Characterization of the retrieved entangled state. The reconstructed density matrices of the input (a) and the output (b) states of the light. From 50.

Figure 19

(Color online) Transmitted and retrieved pulses for different storage times for an echo based memory [private communication from 116]. The small peak at $t\approx 0$ represents a small leakage (nonstored component) of the incoming field, whereas the later peaks are the retrieved field. The emission time of these light pulses is controlled by reversing the sign of an applied electric field halfway during the storage period.

Figure 20

(Color online) Experimental setup for the teleportation of light to atoms. Strong $y$-polarized pulse interacts with atoms and generates an entangled $x$-polarized mode at the upper sideband frequency (inset). This entangled light is overlapped with the pulse to be teleported on a $50∕50$ beam splitter BS after which the Bell measurements are performed. The results of the Bell measurements are fed back onto atoms via rf magnetic coils. From 216.

Figure 21

(Color online) Teleportation results. (a), (b) Two canonical operators of the verifying pulse plotted as a function of the corresponding canonical operators of the input pulse for $2\times {10}^3$ realizations (vacuum units). The slope which is close to $1∕2$ should be multiplied by 2 to account for the attenuation of the verifying pulse on the beam splitter. From the variances of the distributions along the vertical axis the atomic state variances and the fidelity are obtained. (c) A set of input states with $⟨n⟩=5$ and random phases. From 216.