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arXiv:1512.02166 · Proceedings of the National Academy of Sciences

Large conditional single-photon cross-phase modulation

Kristin M. Beck, Mahdi Hosseini, Yiheng Duan, Vladan Vuletić

Published Aug 12, 2016• 83 citations
arXivHTMLPDF

Abstract

Deterministic optical quantum logic requires a nonlinear quantum process that alters the phase of a quantum optical state by π through interaction with only one photon. Here, we demonstrate a large conditional cross-phase modulation between a signal field, stored inside an atomic quantum memory, and a control photon that traverses a high-finesse optical cavity containing the atomic memory. This approach avoids fundamental limitations associated with multimode effects for traveling optical photons. We measure a conditional cross-phase shift of [Formula: see text] (and up to [Formula: see text] by postselection on photons that remain in the system longer than average) between the retrieved signal and control photons, and confirm deterministic entanglement between the signal and control modes by extracting a positive concurrence. By upgrading to a state-of-the-art cavity, our system can reach a coherent phase shift of π at low loss, enabling deterministic and universal photonic quantum logic.

DOI
10.1073/pnas.1524117113

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Deterministic optical quantum logic requires a nonlinear quantum process that alters the phase of a quantum optical state by π through interaction with only one photon. Here, we demonstrate a large conditional cross-phase modulation between a signal field, stored inside an atomic quantum memory, and a control photon that traverses a high-finesse optical cavity containing the atomic memory. This approach avoids fundamental limitations associated with multimode effects for traveling optical photons. We measure a conditional cross-phase shift of [Formula: see text] (and up to [Formula: see text] by postselection on photons that remain in the system longer than average) between the retrieved signal and control photons, and confirm deterministic entanglement between the signal and control modes by extracting a positive concurrence. By upgrading to a state-of-the-art cavity, our system can reach a coherent phase shift of π at low loss, enabling deterministic and universal photonic quantum logic.
Large nonlinearity at the single-photon level can pave the way for the implementation of universal quantum gates. However, realizing large and noiseless nonlinearity at such low light levels has been a great challenge for scientists in the past decade. Here, we propose a scheme that enables substantial nonlinear interaction between two light fields that are both stored in an atomic memory. Semiclassical and quantum simulations demonstrate the feasibility of achieving large cross-phase modulation (XPM) down to the single-photon level. The proposed scheme can be used to implement parity gates from which CNOT gates can be constructed. Furthermore, we present a proof of principle experimental demonstration of XPM between two optical pulses: one stored and one freely propagating through the memory medium. Researchers have developed a new technique that shows promise for constructing optical quantum logic gates. Theoretical simulations performed by Mahdi Hosseini and co-workers from the Australian National University and Macquarie University in Australia show that inducing cross-phase modulation between two single-photon light fields stored in a rubidium atomic memory should provide large phase shifts and thus allow the realization of parity gates and CNOT gates, both of which are needed for quantum computing. The researchers estimate that using cold atoms confined in a dipole trap and short-duration single-photon wavepackets should make it possible to realize phase shifts of the order of 10 mrad — orders of magnitude larger than schemes that employ electromagnetically induced transparency.
A deterministic photon-photon quantum logic gate is a long-standing goal. Building such a gate becomes possible if a light pulse containing only one photon imprints a phase shift of π onto another light field. We experimentally demonstrate the generation of such a π phase shift with a single-photon pulse. A first light pulse containing less than one photon on average is stored in an atomic gas. Rydberg blockade combined with electromagnetically induced transparency creates a phase shift for a second light pulse, which propagates through the medium. We measure the π phase shift of the second pulse when we postselect the data upon the detection of a retrieved photon from the first pulse. This demonstrates a crucial step toward a photon-photon gate and offers a variety of applications in the field of quantum information processing.
Conditional- π phase shift between two photons is essential for entanglement generation and universal quantum logic. For photons, however, direct conditional controls are not possible and must be mediated by nonlinear media. Achieving such operations for photonic polarization qubits has remained difficult due to intrinsically weak photon-photon nonlinearities in atomic systems. Here, we show that a conditional- π phase shift between two weak coherent pulses can be realized via a cavityless closed double- Λ atomic system, where quantum interference between linear and nonlinear atom-photon interactions enables conditional control. By optimizing the interaction parameters, including amplitude and phase compensations, we identify the conditions for conditional- π phase shift between two weak coherent pulses. Experimentally, we observe the conditional- π phase shift with relative output amplitude 0.74 ± 0.06 and phase shift ( 0.95 ± 0.03 ) π between the two-photon amplitudes | H H 〉 and | V V 〉 . A theoretical analysis of Bell-state generation from weak coherent pulses further shows Clauser-Horne-Shimony-Holt inequality violation and nonzero concurrence. Our results clarify both the theoretical requirements and the experimental feasibility of cavityless atom-mediated nonlinearities for photonic quantum logic, establishing a scalable route toward nonlinear quantum photonics.
Optical nonlinearities enable photon-photon interaction and lie at the heart of several proposals for quantum information processing, quantum nondemolition measurements of photons, and optical signal processing. To date, the largest nonlinearities have been realized with single atoms and atomic ensembles. We show that a single quantum dot coupled to a photonic crystal nanocavity can facilitate controlled phase and amplitude modulation between two modes of light at the single-photon level. At larger control powers, we observed phase shifts up to pi/4 and amplitude modulation up to 50%. This was accomplished by varying the photon number in the control beam at a wavelength that was the same as that of the signal, or at a wavelength that was detuned by several quantum dot linewidths from the signal. Our results present a step toward quantum logic devices and quantum nondemolition measurements on a chip.
We study the giant Kerr nonlinear interaction between two ultraweak optical fields in which the cross-phase-modulation is not accompanied by spectral broadening of the interacting pulses. This regime is realizable in atomic vapors, when a weak probe pulse, upon propagating through the electromagnetically induced transparency (EIT) medium, interacts with a signal pulse that is dynamically trapped in a photonic band gap created by spatially periodic modulation of its EIT resonance. We find that large conditional phase shifts and entanglement between the signal and probe fields can be obtained with this scheme. The attainable $\ensuremath{\pi}$ phase shift, accompanied by negligible absorption and quantum noise, is shown to allow a high-fidelity realization of the controlled-phase universal logic gate between two single-photon pulses.
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