Photo-activated Biological Processes As Quantum Measurements

Birgitta Whaley (left) and Atac Imamoglu

Authors: Atac Imamoglu¹, Birgitta Whaley²

Affiliation:
¹Institute of Quantum Electronics, ETH Zurich, Switzerland,
²Berkeley Quantum Information and Computation Center, Department of Chemistry, University of California, Berkeley, USA.

Image credit: Ilya Sinayskiy

Our current understanding of the physical world around us is based on quantum mechanics. It is natural in this framework to argue that at the molecular level, biological processes are also governed by the laws of quantum mechanics. This reasoning in turn implies that at short enough length and/or time scales the dynamics can exhibit counter-intuitive features, such as the molecule/system being in a coherent superposition of distinguishable states. A key question of fundamental interest is whether there are biological systems for which these microscopic dynamical quantum features help or enable the biological function [1-3]. Two processes that have been extensively studied in this context are light harvesting in photosynthesis and sensing of the inclination of the earth’s magnetic field by migrating birds.

Past 2Physics article by Atac Imamoglu :
December 23, 2012: "Observation of Entanglement Between a Quantum Dot Spin and a Single Photon" by Wei-bo Gao, Parisa Fallahi, Emre Togan, Javier Miguel-Sanchez, Atac Imamoglu.

Our work brings a new perspective to the analysis of these processes by embedding them in a quantum measurement context, where the biological system is modelled as a measurement device that is subject to the laws of quantum mechanics (i.e., a quantum meter) [4]. The function of this quantum meter is to measure an external classical stimulus, which is thereby equivalent to the biological sensing of this stimulus. We have analyzed several photo-activated biological processes within this formulation and find that these processes fall into two distinct classes.

In the first category, the measurement interaction induces changes in the system state at a rate that is proportional to the strength of the external stimulus. In this case, we find that while the presence of quantum coherence during the measurement interaction may result in a small enhancement of the rate that increases at most linearly with the increasing coherence time, it is however not essential for the biological function that results from the sensing of this stimulus.

By contrast, in the second category, the measurement interaction does not directly lead to an excitation rate that is proportional to the strength of the external stimulus. Instead, it is the quantum coherent evolution after the optical excitation that controls the sensitivity of the biological system to the stimulus. Most importantly, in this category, unless there is some quantum coherent dynamics after the photoactivation, there is vanishing sensitivity to the signal to be measured. Another difference is that depending on the specific nature of this coherent evolution, more detailed information about the signal than just its strength can be transmitted to the biological receptors.

The extensively studied process of photosynthesis [see, e.g., 1-3, 5-7] as well as the process of human vision [8,9] both belong to the first category. In contrast, the proposed hypothesis of a radical pair mechanism [10,11] for sensing of the inclination of the earth’s magnetic field by migratory birds belongs to the second category. An essential component of this mechanism is the coherent oscillation between singlet and triplet radical pairs in which the paired electrons are separated by several nanometers and are thus formally entangled over non-trivial distances. The chemical reactivity of the radical pair is different in the singlet and triplet states, resulting in a chemical signature of the non-equilibrium quantum dynamics induced by the quantum coherent dynamics.

While much indirect chemical evidence exists for this hypothesis, experimental validation in birds is challenging and, despite many plausibility arguments, no clear evidence for the validity of this hypothesis in migratory birds has been established thus far. It therefore remains an intriguing and open question today, as to whether there are biological sensing processes that can function only if quantum coherence is preserved on some extended time scale.

References:
[1] Graham R. Fleming, Gregory D. Scholes, Yuan-Chung Cheng, “Quantum effects in biology”, Procedia Chemistry, 3, 38 (2011). Abstract.
[2] Neill Lambert, Yueh-Nan Chen, Yuan-Chung Cheng, Che-Ming Li, Guang-Yin Chen, Franco Nori, “Quantum biology”, Nature Physics, 9, 10 (2013). Abstract.
[3] M. Mohseni, Y. Omar, G. Engel, M. Plenio (Eds.), "Quantum effects in biology" (Cambridge University Press, 2014). 
[4] A. Imamoglu, K. B. Whaley, “Photo-activated biological processes as quantum measurements”, Physical Review E, 91,022714 (2015). Abstract.
[5] Rienk van Grondelle, Vladimir I. Novoderezhkin, “Quantum effects in photosynthesis”, Procedia Chemistry, 3, 198 (2011). Abstract.
[6] Konstantin E. Dorfman, Dmitri V. Voronine, Shaul Mukamel, Marlan O. Scully, “Photosynthetic reaction center as a quantum heat engine”, Proceedings of the National Academy of Sciences of USA, 110, 2746 (2013). Abstract.
[7] Aurélia Chenu, Gregory D. Scholes, “Coherence in energy transfer and photosynthesis”, Annual Review of Physical Chemistry, 66, 69 (2015). Abstract.
[8] F. Rieke, D. A. Baylor, “Single-photon detection by rod cells of the retina”, Review of Modern Physics, 70, 1027 (1998). Abstract.
[9] Philipp Kukura, David W. McCamant, Sangwoon Yoon, Daniel B. Wandschneider, Richard A. Mathies,”Structural observation of the primary isomerization in vision with femtosecond-stimulated Raman”, Science, 310, 1006 (2005). Abstract.
[10] Thorsten Ritz, Salih Adem, Klaus Schulten, “A model for photoreceptor-based magnetoreception in birds”, Biophysical Journal, 78, 707 (2000). Full Article.
[11] Kiminori Maeda, Alexander J. Robinson, Kevin B. Henbest, Hannah J. Hogben, Till Biskup, Margaret Ahmad, Erik Schleicher, Stefan Weber, Christiane R. Timmel, P.J. Hore, “Magnetically sensitive light-induced reactions in cryptochrome are consistent with its proposed role as a magnetoreceptor”, Proceedings of the National Academy of Sciences, 109, 4774 (2012). Abstract.

Observation of Entanglement Between a Quantum Dot Spin and a Single Photon

[From left to right] Parisa Fallahi, Atac Imamoglu, Javier Miguel-Sanchez, Wei-bo Gao, Emre Togan















Authors: Wei-bo Gao, Parisa Fallahi, Emre Togan, Javier Miguel-Sanchez, Atac Imamoglu

Affiliation: Institute of Quantum Electronics, ETH Zurich, Switzerland

Entanglement deepens our understanding of fundamental physics. A well-known example is the study of non-local interpretations of quantum mechanics by testing the violation of Bell’s inequality [1]. In the practical side, an interface between a stationary qubit (spin) and a flying qubit (photon) is a basic element to build a distributed quantum network. Moreover, such a network can be used for building a quantum computer, that offers significant speedups in solving certain technologically relevant classes of problems. A realization of distributed quantum computation will use few-qubit quantum processor nodes (spins) connected by photons [2]. A particularly interesting platform is a spin based semiconductor system in which photonic circuits that interconnect the nodes can be fabricated on the same semiconductor chip [3].

In the past few years, considerable efforts have been made to demonstrate entanglement between a spin and a photon. In 2004, the first observation of entanglement between a single trapped atom and a single photon was realized in the group of C. Monroe in Michigan [4]. In 2006 and 2007, the entanglement between a neutral atom and a single photon was realized in the groups of H. Weinfurter [5] G. Rempe [6] in Germany. In 2010, entanglement between an N-V center and a single photon was reported [7]. Despite the appeal of semiconductor based systems the realization of spin-photon entanglement in these systems had been very challenging mainly due to fast transitions and strong decoherence of the quantum dot spins and has only been achieved in 2012. In our work as well as the complementary work of the Yamamoto group at Stanford, the difficulty of measurement was overcome and the first semiconductor spin-photon entanglement was reported [8, 9].

Our experiment focuses on a single electron spin trapped in an InGaAs self-assembled quantum dot. A magnetic field of 0.7 Tesla applied perpendicular to the sample growth direction. The ground states of the quantum dot are identified by the orientation of the electron spin. The basic principle behind the deterministic generation of a spin–photon entangled state is straightforward: following the excitation of the quantum dot into an excited (trion) state, radiative recombination will project the system into an entangled state where the color and polarization of the emitted photon are entangled with the spin of the electron in the ground state. Our measurement process entails suppression of the laser background using cross polarized excitation and collection, thus erasing the polarization information of the quantum dot photons. We therefore focus on the entanglement between the spin qubit and the color (frequency) of the photonic qubit.

To demonstrate entanglement we measure both classical and quantum correlations between the electron spin and the color of the emitted photon. Quantum correlations are demonstrated through observation of oscillations in the emitted photon counts conditioned on detecting a spin in a superposition of up and down spins. By reversing the spin projection direction, we observe a Pi-phase change in the oscillation. These oscillations originate from a phase shift between the two components of the entangled state as the time between photon emission and spin measurement is changed. We calculate an overall entanglement fidelity with a lower bound of 0.67±0.05 , which is above 0.5 and thus constitutes a proof for entanglement in our system.

Semiconductor quantum dots have many advantages compared to the other candidates for optically accessible qubits. For example, majority of the photons are emitted into the zero phonon line making them bright, narrow bandwidth single-photon sources. Also fast spin manipulation of the spin states (~4ps) is possible, and the spontaneous emission time is short (~600ps), making a repetition rate of 76MHz possible in our experiment. There are, however, also drawbacks: the dephasing time of the spin states is about 1ns, limiting the useful time window in the entanglement generation. Moreover, lack of a cycling transition, reduces the likelihood of being able to determine the spin state at a single experimental run, limiting efficient scaling to more spins. Luckily these drawbacks can be overcome by using coupled quantum dot systems that have much richer transition structure and the spin qubits can be more robust against the noisy environment [10]. We aim to achieve spin-spin entanglement in the coupled quantum dot systems in the near future.

References:
[1] Alain Aspect, Philippe Grangier, and Gérard Roger, "Experimental realization of Einstein-Podolsky-Rosen-Bohm gedanken experiment: a new violation of Bell’s inequalities", Physical Review Letters, 49, 91–94 (1982). Abstract.
[2] H. J. Kimble, "Quantum Internet", Nature 453, 1023 (2008). Abstract.
[3] K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, A. Imamoğlu, "Quantum nature of a strongly coupled single quantum dot-cavity system", Nature, 445, 896–899 (2007). Abstract.
[4] B. B. Blinov, D. L. Moehring, L.-M. Duan, C. Monroe, "Observation of entanglement between a single trapped atom and a single photon", Nature 428, 153–157 (2004). Abstract.
[5] Jürgen Volz, Markus Weber, Daniel Schlenk, Wenjamin Rosenfeld, Johannes Vrana, Karen Saucke, Christian Kurtsiefer, Harald Weinfurter, "Observation of entanglement of a single photon with a trapped atom", Physical Review Letters, 96, 030404 (2006). Abstract.
[6] Tatjana Wilk, Simon C. Webster, Axel Kuhn, Gerhard Rempe, "Single-atom single-photon quantum interface", Science, 317, 488–490 (2007). Abstract.
[7] E. Togan, Y. Chu, A. S. Trifonov, L. Jiang, J. Maze, L. Childress, M. V. G. Dutt, A. S. Sørensen, P. R. Hemmer, A. S. Zibrov, M. D. Lukin, "Quantum entanglement between an optical photon and a solid state spin qubit", Nature, 466, 730–734 (2010). Abstract.
[8] W. B. Gao, P. Fallahi, E. Togan, J. Miguel-Sanchez, A. Imamoglu, "Observation of entanglement between a quantum dot spin and a single photon", Nature, 491, 426–430 (2012). Abstract.
[9] Kristiaan De Greve, Leo Yu, Peter L. McMahon, Jason S. Pelc, Chandra M. Natarajan, Na Young Kim, Eisuke Abe, Sebastian Maier, Christian Schneider, Martin Kamp, Sven Höfling, Robert H. Hadfield, Alfred Forchel, M. M. Fejer, Yoshihisa Yamamoto, "Quantum-dot spin–photon entanglement via frequency down conversion to telecom wavelength", Nature, 491, 421–425 (2012). Abstract.
[10] K. M. Weiss, J. M. Elzerman, Y. L. Delley, J. Miguel-Sanchez, A. Imamoğlu, "Coherent Two-Electron Spin Qubits in an Optically Active Pair of Coupled InGaAs Quantum Dots", Physical Review Letters, 109, 107401 (2012). Abstract.

A Step Towards The Realization of A Quantum Network

Ataç Imamoglu (left) and Aymeric Delteil (right)

Authors : Aymeric Delteil, Zhe Sun, Stefan Fält, Atac Imamoglu

Affiliation: Institute of Quantum Electronics, ETH Zurich, Switzerland.

Quantum network architectures consist of local nodes comprising quantum memories that are interconnected using single photons propagating in photonic channels. In such networks, the ability to transfer a quantum bit of information (qubit) from one node to another plays a central role. In a practical implementation, the photonic qubits are generated through spontaneous emission from a matter qubit – embodied for instance by a single atom or ion, a point defect or a quantum dot in a solid-state matrix. The generated photons are then collected in a fiber and sent to another matter qubit using a photonic channel.

Since photonic channels are subject to imperfect collection efficiencies and photon losses, there is a finite probability that such a state transfer based on a single photonic qubit fails. It is therefore suitable to have a heralding signal testifying that the transfer has been successful. Although some basic elements towards such heralded quantum state transfer have already been demonstrated in previous work using various physical systems [1-4], a full node-to-node heralded transfer using single photon qubits has not been achieved to date, mainly due to the dominant role of photon losses.

Using self-assembled semiconductor quantum dots (QDs), we have demonstrated heralded absorption of a neutral (source) QD generated single photonic qubit, by a single-electron charged (target) QD that is located 5 m away [5]. The photonic qubit is thereby transferred and stored in the spin degree of freedom of the single host electron. A successful process is heralded by detection of a subsequent photon that carries no information about the qubit state, which is essential to preserve the coherent quantum superposition.

The principle of our experiment is depicted in fig. 1. The source QD (QD1) is neutral and can be prepared in an arbitrary superposition of two exciton states using a two-color laser beam. This quantum state is encoded in the color of a single photon (flying qubit) generated upon radiative recombination of the QD1 exciton. This flying qubit is collected into a fiber and transferred to the target QD. Amongst the wide variety of QDs that are randomly formed during the growth of the sample, the target QD has been carefully selected to have a specific energy level scheme presenting two transitions of identical energies, such that photons emitted after absorption of the photonic qubit carry no information about the decay path. As a consequence, if the spin state is initially prepared in the superposition state |up> + |down>, upon absorption of the photonic qubit and detection of the subsequent photon, the electron spin ends in the qubit state generated by the laser excitation of the source QD.

Figure 1 : (Click on the image to view with higher resolution) Principle of the state transfer protocol based on heralded absorption of a single photon qubit.

Implementing such an experiment is particularly challenging due to finite collection efficiencies and losses in the optical elements along the chain. One of the key elements that have allowed our realization is the use of a photonic structure enabling efficient extraction of the emitted photons. More specifically, the QDs are embedded in a planar cavity and the cavity output is collected using a solid immersion lens placed on top of the sample, ensuring that about 20% of the photons from each QD are collected by the first lens. The use of sensitive superconducting single photon detector with very low dark counts as well as crossed-polarization detection to suppress the strong pump laser light and background scattering have allowed us to demonstrate heralded absorption where we detected up to about 100 successful events per second. We demonstrated that the final state of the destination quantum dot spin is correlated with the initial state of the photon (or the target QD exciton) by measuring time-resolved photon coincidences.

Our scheme can be extended to realize spin-to-spin state transfer, or to generate heralded distant entanglement between two QD spins [6]. It can also be used to connect dissimilar physical systems in the context of hybrid quantum networks [7].

References:
[1] Stephan Ritter, Christian Nölleke, Carolin Hahn, Andreas Reiserer, Andreas Neuzner, Manuel Uphoff, Martin Mücke, Eden Figueroa, Joerg Bochmann, Gerhard Rempe, “An elementary quantum network of single atoms in optical cavities”, Nature, 484, 195 (2012). Abstract.
[2] Christoph Kurz, Michael Schug, Pascal Eich, Jan Huwer, Philipp Müller, Jürgen Eschner, “Experimental protocol for high-fidelity heralded photon-to-atom quantum state transfer”, Nature Communications, 5, 5527 (2014). Abstract.
[3] Norbert Kalb, Andreas Reiserer, Stephan Ritter, Gerhard Rempe, “Heralded Storage of a Photonic Quantum Bit in a Single Atom”, Physical Review Letters, 114, 220501 (2015). Abstract.
[4] Sen Yang, Ya Wang, D. D. Bhaktavatsala Rao, Thai Hien Tran, Ali S. Momenzadeh, M. Markham, D. J. Twitchen, Ping Wang, Wen Yang, Rainer Stöhr, Philipp Neumann, Hideo Kosaka, Jörg Wrachtrup, “High-fidelity transfer and storage of photon states in a single nuclear spin”, Nature Photonics, 10, 507 (2016). Abstract.
[5] Aymeric Delteil, Zhe Sun, Stefan Fält, Atac Imamoğlu, “Realization of a Cascaded Quantum System: Heralded Absorption of a Single Photon Qubit by a Single-Electron Charged Quantum Dot”, Physical Review Letters, 118, 177401 (2017). Abstract.
[6] D. Pinotsi and A. Imamoglu, “Single Photon Absorption by a Single Quantum Emitter”, Physical Review Letters, 100, 093603 (2008). Abstract.
[7] H. M. Meyer, R. Stockill, M. Steiner, C. Le Gall, C. Matthiesen, E. Clarke, A. Ludwig, J. Reichel, M. Atatüre, M. Köhl, “Direct Photonic Coupling of a Semiconductor Quantum Dot and a Trapped Ion”,  Physical Review Letters, 114, 123001 (2015). Abstract.

Single Photon Transistor Mediated by Rydberg Interaction

From Left to Right: Hannes Gorniaczyk, Christoph Tresp, Johannes Schmidt, Ivan Mirgorodskiy, Sebastian Hofferberth

Authors: Christoph Tresp, Ivan Mirgorodskiy, Hannes Gorniaczyk, Sebastian Hofferberth 

Affiliation:
Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universität Stuttgart, Germany.

Link to Rydberg Quantum Optics, Emmy Noether Group >>

Introduction:

In analogy to their electronic counterparts, all-optical switches and transistors are required as basic building blocks for both classical and quantum optical information processing [1,2]. Reaching the fundamental limit of such devices, where a single gate photon modifies the transmission or phase accumulation of multiple source photons, requires strong effective interaction between individual photons. Engineering sufficiently strong optical nonlinearities to facilitate photon-photon interaction is one of the key goals of modern optics. Immense progress towards this goal has been made in a variety of systems in recent years. Most prominent so far are cavity QED experiments where a high finesse resonator enhances the interaction between light and atoms [3,4] or artificial atoms [5,6].

In this work, we demonstrate a free-space all-optical transistor operating on the single photon level using a novel approach to realize effective photon-photon interaction [7], which is based on mapping the strong interaction of Rydberg atoms [8] onto slowly travelling photons using electromagnetically induced transparency [9]. This technique has already been used to demonstrate highly efficient single-photon generation [10], attractive interaction between single photons [11], entanglement generation between light and atomic excitations [12], and most recently single-photon all-optical switching [13].

However, demonstration of amplification, that is, controlling many photons with a single one, has so far only been achieved in a cavity QED setup [14]. Gain > 1 is one of the key properties of the electric transistor that lies at the heart of its countless applications. In our experiment, we demonstrate an all-optical transistor with optical gain G > 10 [15]. Similar results have been obtained by the group of G. Rempe, their results have been published in parallel to ours [16].

Experiment:

The level scheme and geometry of our transistor are illustrated in Fig. 1 (a, b). Photons in the weak gate pulse are stored as Rydberg excitations in an atomic ensemble by coupling the ground state |g> to the Rydberg state |r_g> via the strong gate control field. After this storage process, a second weak pulse, the source pulse, is sent through the medium at reduced velocity due to EIT provided by the source control laser coupling to the Rydberg state |r_s>.

FIG. 1: (a) Level scheme, (b) simplified schematic, and (c) pulse sequence of our all-optical transistor. (d) The absorption spectrum for the source field (dots) over the full intermediate state absorption valley shows the EIT window on resonance; the gate field spectrum (circles) is taken around the two-photon resonance at Δ = 40 MHz. The solid lines are fits to the EIT spectra.

In the absence of the gate pulse, source photons travel through the transparent medium (Fig. 1d). If a gate photon has been stored, the strong interaction between the two Rydberg states destroys the EIT condition for the source photons in the medium, resulting in absorption. To observe this conditional switching, we record the number of transmitted source photons in a time interval tint after the gate excitation pulse, cf. Fig. 1 (c). For the experimental realization of this scheme, we prepare 2.5 X 10^{4 87}Rb atoms at a temperature of T = 40 µK in an optical dipole trap. All four lasers required for the transistor scheme are focused into this medium along a single direction (Fig. 1b). The weak gate and source pulses are recorded on single photon counters.

Results:

We first investigate the relative attenuation of a weak source pulse as a function of mean incident gate photons. In Fig. 2 (a) we plot the switch contrast in the source beam transmission as a function of the mean incoming gate photon number. For an average gate photon number of N_g,in = 1.04(3), we observe a switch contrast C_coh = 0.39(4). The switch contrast is mainly determined by the Poissonian statistics of our coherent gate photons, which sets a fundamental upper bound. In other words, a perfect switch with coherent gate photons has a switch contrast C_coh = 1 - exp(-N_g,in) (dashed line in Fig. 2 (a)). How close our switch approaches this fundamental limit depends on the gate photon storage efficiency and the source attenuation caused by a single gate excitation. In Fig. 2 (b) we plot the switch contrast versus the mean number of stored gate photons, which is smaller than the mean incident gate photon number due to not perfect gate photon storage. Finally, by again taking the Poissonian statistics of the input light into account, we extrapolate the switch contrast caused by a single stored excitation to be C_exc = 0.9.

FIG. 2: Switch contrast (red) as function of (a) mean number of incident gate photons and (b) mean number of stored photons. The dashed line indicates the fundamental limit set by the photon statistics of the coherent gate input. Black data points represent the calculated switch contrast expected for (a) one-, two- and three-photon Fock input states or (b) deterministic single and two stored gate excitations.

Next, we investigate how many source photons can be switched by our system. To quantify the gate-induced change in source transmission, we consider the optical gain
G = N_s,out^{no gate} - N_s,out^{with gate}. In Fig. 3 (a), we plot the measured optical gain for an average input of gate photons N_g,in = 0.75(3). For this gate input, we observe a maximum optical gain G(N_g,in = 0.75) = 10(1). Further increase of the optical gain at fixed gate input is limited by the self-blockade of the source beam, which results in nonlinear source transmission even in the absence of gate photons [7, 17]. The red (blue) data points in Fig. 3 (b) show the source photon transfer function when N_g,in = 0 (N_g,in = 0.75(3)). For the given integration time the source transmission saturates at 46 photons, which limits the maximum gain we can observe. On the other hand, the self-nonlinearity of the source light does not affect the transistor performance, we observe a constant switch contrast of C = 0.22(3), consistent with the mean gate input, even for incoming source photons up to ~250. Based on this robustness, we can again extrapolate the transistor performance for a true single photon gate input (Fig. 3 green line) and a single stored excitation (grey line). For a single excitation, we calculate the maximally achievable optical gain of our current system as G_st = 28(2).

FIG. 3: (a) Optical gain of our transistor, measured for coherent gate input N_g,in = 0.75(3) (blue data), and extrapolated to single photon Fock state input (green line), and single stored excitation (black line). (b) Source photon transfer function without (red) and with coherent gate input N_g,in = 0.75(3) (blue). We observe a constant switch contrast between the two data sets over the whole source input range. The green (black) solid line are again the estimated behavior of the system for a single-photon Fock input state (a single stored excitation). Shaded regions are error estimates.

Discussion and outlook:

In summary, we have demonstrated a free-space single photon transistor based on two-color Rydberg interaction. Further improvements of our system could enable a high optical gain, high efficiency optical transistor, so far only realized in a cavity QED setup [14]. One approach to overcome the self-nonlinearity of the source photons has already been demonstrated by the Rempe group, who employ a two-color Förster resonance in their transistor scheme [16].

A key step towards turning our transistor into device which can perform quantum operations on single or few photons is the retrieval of gate photon(s) after the switch process, which could enable multi-photon entanglement protocols and creation of non-classical light-states with large photon numbers. Finally, our system is a highly sensitive probe for studying Rydberg interaction on the few-particle level [18]. In particular, the combination of two independently controlled Rydberg-EIT schemes enables novel fields of study, such as the interplay between slow light propagation and Rydberg exchange interaction [19], or realization of a two-photon phase gate based on Rydberg-polariton collision [20].

References:
[1] H. John Caulfield and Shlomi Dolev, "Why future supercomputing requires optics". Nature Photonics, 4, 261 (2010). Abstract.
[2] Jeremy L. O'Brien, Akira Furusawa, Jelena Vuckovic, "Photonic quantum technologies". Nature Photonics, 3, 687 (2009). Abstract.
[3] K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup, H. J. Kimble, "Photon blockade in an optical cavity with one trapped atom". Nature, 436, 87 (2005). Abstract.
[4] Tatjana Wilk, Simon C. Webster, Axel Kuhn, Gerhard Rempe, "Single-Atom Single-Photon Quantum Interface". Science, 317, 488 (2007). Abstract.
[5] P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, Lidong Zhang, E. Hu, A. Imamoglu, "A Quantum Dot Single-Photon Turnstile Device". Science, 290, 2282 (2000). Abstract.
[6] Dirk Englund, Andrei Faraon, Ilya Fushman, Nick Stoltz, Pierre Petroff, Jelena Vuckovic, "Controlling cavity reflectivity with a single quantum dot". Nature, 450, 857 (2007). Abstract.
[7] J. D. Pritchard, D. Maxwell, A. Gauguet, K. J. Weatherill, M. P. A. Jones, C. S. Adams, "Cooperative Atom-Light Interaction in a Blockaded Rydberg Ensemble". Physical Review Letters, 105, 193603 (2010). Abstract.
[8] M. Saffman, T. G. Walker, K. Mølmer, "Quantum information with Rydberg atoms". Review of Modern Physics, 82, 2313 (2010). Abstract.
[9] Michael Fleischhauer, Atac Imamoglu, Jonathan P. Marangos, "Electromagnetically induced transparency: Optics in coherent media". Review of Modern Physics, 77, 633 (2005). Abstract.
[10] Y. O. Dudin and A. Kuzmich, "Strongly Interacting Rydberg Excitations of a Cold Atomic Gas". Science 336, 887 (2012). Abstract.
[11] Ofer Firstenberg, Thibault Peyronel, Qi-Yu Liang, Alexey V. Gorshkov, Mikhail D. Lukin, Vladan Vuletić, "Attractive photons in a quantum nonlinear medium". Nature, 502, 71 (2013). Abstract.
[12] L. Li, Y. O. Dudin, and A. Kuzmich, "Entanglement between light and an optical atomic excitation". Nature, 498, 466 (2013). Abstract.
[13] Simon Baur, Daniel Tiarks, Gerhard Rempe, Stephan Dürr, "Single-Photon Switch Based on Rydberg Blockade". Physical Review Letters, 112, 073901 (2014). Abstract.
[14] Wenlan Chen, Kristin M. Beck, Robert Bücker, Michael Gullans, Mikhail D. Lukin, Haruka Tanji-Suzuki, Vladan Vuletić, "All-Optical Switch and Transistor Gated by One Stored Photon". Science 341, 768 (2013). Abstract.
[15] H. Gorniaczyk, C. Tresp, J. Schmidt, H. Fedder, S. Hofferberth, "Single-Photon Transistor Mediated by Interstate Rydberg Interactions". Physical Review Letters, 113, 053601 (2014). Abstract.
[16] Daniel Tiarks, Simon Baur, Katharina Schneider, Stephan Dürr, Gerhard Rempe, "Single-Photon Transistor Using a Förster Resonance". Physical Review Letters, 113, 053602 (2014). Abstract.
[17] Thibault Peyronel, Ofer Firstenberg, Qi-Yu Liang, Sebastian Hofferberth, Alexey V. Gorshkov, Thomas Pohl, Mikhail D. Lukin, Vladan Vuletić, "Quantum nonlinear optics with single photons enabled by strongly interacting atoms". Nature, 488, 57 (2012). Abstract.
[18] L. Béguin, A. Vernier, R. Chicireanu, T. Lahaye, A. Browaeys, "Direct Measurement of the van der Waals Interaction between Two Rydberg Atoms". Physical Review Letters, 110, 263201 (2013). Abstract.
[19] Weibin Li, Daniel Viscor, Sebastian Hofferberth, Igor Lesanovsky, "Electromagnetically Induced Transparency in an Entangled Medium". Physical Review Letters, 112, 243601 (2014). Abstract.
[20] Alexey V. Gorshkov, Johannes Otterbach, Michael Fleischhauer, Thomas Pohl, Mikhail D. Lukin, "Photon-Photon Interactions via Rydberg Blockade". Physical Review Letters, 107, 133602 (2011). Abstract.