# Quantum memory for long-distance and multiphoton entanglement

Quantum information science is an intriguing example where purely fundamental and even philosophical research has led to new technologies. Indeed, quantum physics, which explains the atomic behavior underpinning these innovations, provides qualitatively new and powerful concepts of communication and information processing. In this small world, single photons (particles of light) are the most promising messengers because they can be easily manipulated. Like a coin tossed into the air that could be either heads or tails until it lands, a photon can exist in a superposition of two or more states.

We say that the photon has simultaneously horizontal and vertical polarization. When the superposition is extended to more than one particle, it is called entanglement. Before measurement, neither of the photons has a definite polarization, and the result of a single measurement on either of them is always completely random. As soon as the polarization of one of the photons is determined, however, its distant entangled ‘twin’ acquires a well-defined polarization.^{1} These quantum phenomena, which Albert Einstein called ‘spooky action at a distance,‘ have the potential to enable absolutely secure cryptography and very powerful computers.

The bigger and more complex the entangled systems become, the more surprising and more rich the quantum phenomena appear. Three and four entangled particles already give rise to more powerful communication protocols and even to some elementary blocks of future computers, including the new concept of one-way quantum computing using highly-entangled cluster states.^{2} A cluster state can be seen as a superposition of all possible answers of the computation's outcome, similar to novelist Jorge Luis Borges' library of all possible books. Simple measurements on the state will then create the right outcome with certainty. So far, however, all experiments have been limited to few-photon entangled states due to the unavailability of controlled and efficient single-photon sources.^{3}

**Single-photon generation using quantum memory**

The current state-of-the-art technology for producing single photons is so-called spontaneous parametric down-conversion (SPDC) (see Figures 1 and 2). But SPDC has the disadvantage of emitting randomly entangled photon pairs, which reduces exponentially the emission rate of several photon pairs at the same time, as required to generate multiphoton cluster states. One way around this limitation is to use different sources together with quantum memory, which makes it possible to store an atomic excitation. Over the past few years, great progress has been made in this field from a number of different directions.^{5–11} The basic idea and setup of experiments dealing with atomic ensembles (very large numbers of atoms or atom gas) are based on the theoretical work of Duan, Lukin, Cirac, and Zoller^{12} and are illustrated in Figure 3.

To conditionally generate single photons (in other words, we know when we get them) the atomic ensemble is initially prepared in the ground state |*g*〉 (the structure of a ^{87}Rb atom in zero magnetic field can be pictured as a three-level atom with |*g* 〉=|5^{2}*S*_{1/2}, *F*=1 〉, |s 〉=|5^{2}*S*_{1/2}, *F*=2 〉, and |*e*〉 = |5^{2}*P*_{1/2}, *F*′=1 〉 and |5^{2}*P*_{1/2}, *F*′=2 〉. Atomic spin excitations to the state |*s*〉 are produced via spontaneous Raman scattering, induced by a laser beam referred to as the write laser. In this process, correlated pairs of frequency-shifted ‘Stokes’ photons and flipped atomic spins are created via Raman transitions into the state |*s*〉. Energy and momentum conservation ensure that by detecting a Raman-scattered Stokes photon, the atomic ensemble is prepared in a state with exactly one flipped spin quantum in a well-defined spin-wave mode. Conditioned upon detecting a single Stokes photon, the stored single spin-wave quantum is later coherently converted into a single-photon anti-Stokes pulse using electromagnetically induced transparency (EIT) by applying a second near-resonant retrieve laser beam^{8,13} for converting the atomic excitation from state |*s*〉 into a single anti-Stokes photon. Thus, the direction, bandwidth, and central frequency of the single-photon anti-Stokes pulse are determined by the direction, intensity, and frequency of the retrieve laser.

All laser beams and signal modes are aligned to be collinear to reduce the effects of Doppler shifts of frequencies at room temperature. The retrieve laser and the anti-Stokes field are counter-propagating in respect to the write laser and the Stokes field inside the magnetically shielded atomic ensemble. The single spatial mode, defined by the detection fibers and by the optics, has a diameter of 200μ m at the center of the ensemble. An etalon (^{85}Rb cell) is used to reflect (absorb) the fraction of the write (retrieve) laser intensity not filtered by the polarizing beamsplitters. The atomic ensemble is a 4.5cm-long isotopically pure ^{87}Rb vapor cell with 7torr neon buffer gas (see Figure 4).

To quantify the properties of the single-photon source, the anti-Stokes photons are studied using a Hanbury–Brown–Twiss-type setup, which allows us to measure normalized second-order correlation functions, *g*^{(2)}, which are ideally *g*^{(2)}=0 for a pure single-photon state and *g*^{(2)}=1 for a coherent state. Figure 5 shows a measurement of the photon-number fluctuations of the anti-Stokes field conditioned on detecting a single Stokes photon, as a function of the detection probability *p*η_{S} in the Stokes channel, where *p* is the probability that a Stokes photon is emitted and η_{S} is the transmission probability between the source ensemble and the Stokes detectors. As *p* becomes much smaller than unity, we observe substantial suppression of the conditional intensity fluctuations in the anti-Stokes pulses compared to the classical limit of unity.

**Conclusion **

Our results demonstrate that Raman scattering and the use of EIT in room-temperature atomic ensembles make it possible to generate states that are close to single photons. The fact that the demonstrated storage time of the quantum memory is on the order of several microseconds may mean that scalable single-photon sources are brought a step closer, and the implementation of large-scale quantum communication and computation may not be so far out of reach.

Philip Walther is a postdoctoral researcher and is currently working on experiments for the realization of quantum repeaters using atomic ensembles.

Alex Nemiroski is a graduate student and is working on the experimental realization of quantum repeaters using atomic ensembles.

Alexey Gorhskov is a graduate student in theoretical physics and is responsible for the theoretical support of the quantum repeater experiments.

Alexander Zibrov is a senior researcher at Harvard University and best known for his achievements in atomic physics and spectroscopy.

Mikhail Lukin is professor of physics at Harvard University. His experimental and theoretical research is in the areas of quantum optics and atomic physics. The emphasis is on studies of quantum systems consisting of interacting photons, atoms, molecules, and electrons coupled to realistic environments.