Optoelectronics & Communications
Quantum memory for longdistance and multiphoton entanglement
Philip Walther, Alex Nemiroski, Alexey Gorshkov, Alexander Zibrov, and Mikhail Lukin
The possibility of generating single photons at room temperature might solve the scalability problem associated with quantum communication and computing.
3 April 2008, SPIE Newsroom. DOI: 10.1117/2.1200803.1072
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 welldefined 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 oneway quantum computing using highlyentangled 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 fewphoton entangled states due to the unavailability of controlled and efficient singlephoton sources.^{3} Figure 1. Schematic of noncollinear type II parametric downconversion using a βbarium borate (βBBO) crystal. Extraordinary V〉 photons of a certain wavelength emerge on the upper cone, ordinary H〉 on the lower cone. The intersections are unpolarized with a fixed relative phase (φ) and display polarization entanglement after proper compensation of the birefringent delay incurred in the downconversion crystal. e^{iφ}: Euler description of the relative phase. Singlephoton generation using quantum memory The current stateoftheart technology for producing single photons is socalled spontaneous parametric downconversion (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. Figure 2. Schematic drawing of the setup for generating fourphoton cluster states without quantum memory. A UV laser passes through the βBBO crystal, is reflected at the pump mirror Δ1, and passes through the crystal again. The coherent overlap of all modes, a1–a2 and b1–b2, at the two polarizing beamsplitters (PBS) allows for the generation of fourphoton cluster states. ^{4} EPRPair: Entangled photon pair. Comp.: Compensator. Pol.: Polarizer. D_{A3}, D_{A4}, D_{B3}, D_{B4}: Dectectors. a3, a4, b3, b4: Paths of the photons after the PBS. Figure 3. ^{87}Rb (rubidium) atoms can be pictured as threelevel atoms, with the ground state g〉, the excited state e〉, and the metastable state s〉, which might be two different hyperfine states F=1 and F=2. The (write, retrieve) laser couples the (g〉 −e〉, s〉 −e〉) transition of the source atoms. The electromagnetically induced transparency (EIT) control laser couples the s〉 −e〉 transition of the target atoms. APD: avalanche photodiode. 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 threelevel 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 frequencyshifted ‘Stokes’ photons and flipped atomic spins are created via Raman transitions into the state s〉. Energy and momentum conservation ensure that by detecting a Ramanscattered Stokes photon, the atomic ensemble is prepared in a state with exactly one flipped spin quantum in a welldefined spinwave mode. Conditioned upon detecting a single Stokes photon, the stored single spinwave quantum is later coherently converted into a singlephoton antiStokes pulse using electromagnetically induced transparency (EIT) by applying a second nearresonant retrieve laser beam^{8,13} for converting the atomic excitation from state s〉 into a single antiStokes photon. Thus, the direction, bandwidth, and central frequency of the singlephoton antiStokes 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 antiStokes field are counterpropagating 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 4.5cmlong isotopically pure ^{87}Rb vapor cell with 7torr neon buffer gas (see Figure 4). Figure 4. Experimental setup of the roomtemperature quantum memory. BS: Beamsplitter. S1,S2 (AS1,AS2): Avalanche photodetectors for the Stokes (antiStokes) channel. Stokes and antiStokes refer to photons that are emitted when an electron is transferred from one energy level to another, in a process called Raman scattering. To quantify the properties of the singlephoton source, the antiStokes photons are studied using a Hanbury–Brown–Twisstype setup, which allows us to measure normalized secondorder correlation functions, g^{(2)}, which are ideally g^{(2)}=0 for a pure singlephoton state and g^{(2)}=1 for a coherent state. Figure 5 shows a measurement of the photonnumber fluctuations of the antiStokes field conditioned on detecting a single Stokes photon, as a function of the detection probability pη_{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 antiStokes pulses compared to the classical limit of unity. Figure 5. AntiStokes fluctuations, conditioned on detection of a single Stokes photon, are characterized by the correlation function , where is the number operator for detector (AS1,AS2). The dashed line represents the classical limit of g^{(2)} (AS  n_{S}=1)=1. Measurements are shown for three values of the Stokes channel transmission: η _{S}=0.08 (red triangles), η _{S}=0.14 (blue diamonds), and η _{S}=0.27 (green squares). Solid lines represent a theoretical model for η _{S} equal to 0.08, 0.14, and 0.27, respectively. For this data, source ensemble temperature ≈26°C. Conclusion Our results demonstrate that Raman scattering and the use of EIT in roomtemperature 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 singlephoton sources are brought a step closer, and the implementation of largescale quantum communication and computation may not be so far out of reach.
Philip Walther, Alex Nemiroski, Alexey Gorshkov Physics Department, Harvard University Cambridge, MA 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 Zibrow Physics Department Harvard University Cambridge, MA Division of Quantum Electronics Lebedev Institute of Physics Moscow, Russia Alexander Zibrov is a senior researcher at Harvard University and best known for his achievements in atomic physics and spectroscopy. Mikhail Lukin Physics Department Harvard University Cambridge, MA HarvardSmithsonian Center for Astrophysics Cambridge, MA 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.
References: 4. P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, A. Zeilinger, Experimental oneway quantum computing, Nature 434, pp. 169176, 2005.

