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Physical Review A

Cross-phase modulation and entanglement in a compound gradient echo memory

Shuangshuang Fu, Andre R. R. Carvalho, Michael Hush, M. R. James

Published Feb 4, 2016• 6 citations
Publisher

Abstract

We present a theoretical model for a Kerr-like interaction between two registers of a compound gradient echo memory (GEM). This type of interaction is known to generate cross-phase modulation (XPM) between optical fields, an effect that is limited by the typically small values of nonlinearities in crystals. Here we show that in GEM systems the phase shift increases linearly with the interaction time and quadratically with the strength of the field. Increasing storage (interaction) times would then lead to stronger XPM effects even with fields with very low intensity. This interaction also generates two other effects: entanglement between the registers, which depends on the strength of the interaction and its spatial profile, and an interaction-induced gradient. We show that the latter produces leakage during the storage stage depending on the shape of the stored pulses, an undesirable consequence that can be minimized by carefully designing the temporal profile of the input fields.

DOI
10.1103/physreva.93.023809

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We present a theoretical model for a Kerr-like interaction between two registers of a compound gradient echo memory (GEM). This type of interaction is known to generate cross-phase modulation (XPM) between optical fields, an effect that is limited by the typically small values of nonlinearities in crystals. Here we show that in GEM systems the phase shift increases linearly with the interaction time and quadratically with the strength of the field. Increasing storage (interaction) times would then lead to stronger XPM effects even with fields with very low intensity. This interaction also generates two other effects: entanglement between the registers, which depends on the strength of the interaction and its spatial profile, and an interaction-induced gradient. We show that the latter produces leakage during the storage stage depending on the shape of the stored pulses, an undesirable consequence that can be minimized by carefully designing the temporal profile of the input fields.
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. We present a proposal for using quantum memory to enhance the cross-phase modulation (XPM) of two optical fields. Our memory, which is based on the gradient echo memory (GEM) scheme, maps the optical fields into Fourier transformed polaritonic excitations in an atomic ensemble. We show that nonlinear interactions can be induced in GEM. Due to the slowing down and subsequent storage of light fields within a memory, nonlinear interaction time between the fields can be extended resulting in an enhancement of the effective nonlinearity. We present results showing noiseless cross-phase modulations and discuss plans to further increase the cross-phase modulation strength to a level useful for implementing quantum gates.
Quantum memories for light lie at the heart of long-distance provably-secure communication [1], while containing the potential to help break current encryption methods [2], and allow better measurement of quantities than ever before [3]. Demand for a functioning quantum memory is therefore at a premium. Unfortunately, the same properties of light that make it such an effective carrier of quantum information make it difficult to store. Furthermore, by the laws of quantum mechanics, storage must be achieved without measurement to preserve the quantum state. A quantum memory needs to have an efficiency approaching unity without adding noise to the state, and storage times from milliseconds to seconds. Ideally it would also have a high bandwidth and be able to store many pieces of information simultaneously. Many different techniques are currently being developed and much experimental progress has been made over the past few years, with: efficiencies approaching 90% [4]; storage times of over seconds [5]; bandwidths of gigahertz [6, 7]; and over 1000 pieces of information stored at one time [8]. These results were, however, achieved using different memory schemes in different storage media. The challenge now is to reproduce these results with one memory. This thesis focuses on extending the gradient echo memory (GEM) scheme, which shows great promise due to the high efficiencies achieved (87%) [4]. GEM has also been used to demonstrate temporal compression and stretching of pulses, as well as a capacity to arbitrarily resequence stored information [9] and the interference of initially time-separated pulses [10]. Firstly, we demonstrate the noiseless nature of GEM storage in a warm vapour cell to prove that the output from the memory is the best-possible copy of the input allowed by quantum mechanics. We show GEM’s ability to coherently and precisely spectrallymanipulate stored information by having fine control over the memory’s frequency gradient, with potential applications for dynamic conditioning of information inside quantum networks [11]. We demonstrate cross-phase modulation of a stored light pulse with an additional optical field, a process with applications in quantum computing [12]. We also carry out storage of different spatial modes and arbitrary images, demonstrating the potential for orders of magnitude improvement in storage capacity. We then switch from warm vapour cells to cold atomic ensembles to improve the storage time of GEM, seeing a maximum coherence time of 350 μs (seven times that of the warm vapour system) and achieving efficiencies of up to 80%, on a par with the highest efficiency achieved with a cold atomic ensemble [13]. In the process we developed an ultra-dense cold atomic cloud with potential applications in a range of quantum optics experiments. Cold atoms, and the small volumes they occupy, also allowed us to develop an alternative to using magnetic field gradients for our alkali-atom memories in the form of a light-field gradient. This holds promise for extremely fast gradient switching and fine control over the gradient. We also present a digital locking code with application in a range of quantum optics experiments.
Abstract Strong nonlinear interactions between single photons have important applications in optical quantum information processing. Demonstrations of these interactions in cold atomic ensembles have largely been limited to exploiting slow light generated using electromagnetically induced transparency (EIT). However, these EIT implementations have limited achievable phase shifts due to spontaneous emission. Here, we demonstrate and characterize a scheme free from these limitations using gradient echo memory with inferred single photon phase shifts of 0.07 ± 0.02 μrad. Excellent agreement with theoretical modelling was observed. Degradation of memory efficiency was observed for large phase shifts but strategies to overcome that are presented.
The burgeoning fields of quantum computing and quantum key distribution have created a demand for a quantum memory. The gradient echo memory (GEM) is one such scheme that can boast efficiencies approaching unity. Here we investigate the ability of GEM to spectrally manipulate light pulses stored in the memory. Spectral manipulation is important for pulse compression sideband extraction, and matching of pulse spectra to resonant and spectroscopic systems, as well as the potential to increase qubit rates in quantum communications networks. We present both theoretical and experimental results demonstrating the ability to shift the frequency, as well as spectrally compress or expand a pulse. Also the ability of GEM to recall different frequency components of a pulse at different times, and interfere two initially time separated pulses that are stored in the memory, are shown.
The burgeoning fields of quantum computing and quantum key distribution have created a demand for a quantum memory. The gradient echo memory (GEM) is one such scheme that can boast efficiencies approaching unity. Here we investigate the ability of GEM to spectrally manipulate light pulses stored in the memory. Spectral manipulation is important for pulse compression sideband extraction, and matching of pulse spectra to resonant and spectroscopic systems, as well as the potential to increase qubit rates in quantum communications networks. We present both theoretical and experimental results demonstrating the ability to shift the frequency, as well as spectrally compress or expand a pulse. Also the ability of GEM to recall different frequency components of a pulse at different times, and interfere two initially time separated pulses that are stored in the memory, are shown.
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.