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Continuous-time cross-phase modulation and quantum computation

Jeffrey H. Shapiro, Mohsen Razavi

Published Jan 1, 2006• 117 citations
OpenAlex

Abstract

Abstract. The weak nonlinear Kerr interaction between single photons and intense laser fields has been recently proposed as a basis for distributed optics-based solutions to few-qubit applications in quantum communication and computation. Here, we analyze the above Kerr interaction by employing a continuous-time multi-mode model for the input/output fields to/from the nonlinear medium. In contrast to previous single-mode treatments of this problem, our analysis takes into account the full temporal content of the free-field input beams as well as the non-instantaneous response of the medium. The main implication of this model, in which the cross-Kerr phase shift on one input is proportional to the photon flux of the other input, is the existence of phase noise terms at the output. We show that these phase noise terms will degrade the performance of the parity gate proposed by Munro, Nemoto, and Spiller [1].Continuous-time cross-phase modulation and quantum computation 2 1.

Related papers

Continuous-time cross-phase modulation and quantum computation

Jeffrey H. Shapiro, Mohsen Razavi

The weak nonlinear Kerr interaction between single photons and intense laser fields has been recently proposed as a basis for distributed optics-based solutions to few-qubit applications in quantum communication and computation. Here, we analyse the above Kerr interaction by employing a continuous-time multi-mode model for the input/output fields to/from the nonlinear medium. In contrast to previous single-mode treatments of this problem, our analysis takes into account the full temporal content of the free-field input beams as well as the non-instantaneous response of the medium. The main implication of this model, in which the cross-Kerr phase shift on one input is proportional to the photon flux of the other input, is the existence of phase noise terms at the output. We show that these phase noise terms will preclude satisfactory performance of the parity gate proposed by Munro et al (2005 New J. Phys. 7 137).

arXiv:quant-ph/0612086•New Journal of Physics•Jan 25, 2007•149 citations

Kerr-induced phase noise in quantum parity gates

Mohsen Razavi, Jeffrey H. Shapiro

Quantum parity gates that use weak nonlinearity between single photons and intense coherent pulses are analyzed using a continuous-time model for cross-phase modulation. An inevitable phase noise is shown to degrade gate fidelity.

Quantum Electronics and Laser Science Conference•May 1, 2007•0 citations

Two photons co- and counterpropagating through N cross-Kerr sites

Daniel J. Brod, Joshua Combes, Julio R. Gea-Banacloche

A cross-Kerr interaction produces a phase shift on two modes of light proportional to the number of photons in both modes and is sometimes called cross-phase modulation. Cross-Kerr nonlinearities have many applications in classical and quantum nonlinear optics, including the possibility of a deterministic and all-optical controlled-phase gate. We calculate the one- and two-photon $S$ matrices for fields propagating in a medium where the cross-Kerr interaction is spatially distributed at discrete interaction sites comprised of atoms. For the interactions considered, we analyze the cases where the photons copropagate and counterpropagate through the medium and give a physical interpretation to the differences between the two cases. Finally, we obtain the $S$ matrix in the limit of infinitely long chains, showing that it corresponds to a perfect controlled-phase operation.

arXiv:1604.03914•Physical Review A•Aug 18, 2016•37 citations

Spectral Effects of Fast Response Cross Kerr Non-Linearity on Quantum Gate

Patrick M. Leung, Timothy C. Ralph, William J. Munro +1 more

According to idealized models, a strong Kerr non-linearity may be used to build optical quantum gates for optical quantum information processing by inducing conditional phase shifts on quantum states. Recently, Shapiro (PRA 73, 062305 (2006)) argued that for a Kerr medium with non-instantaneous but fast response, essentially no phase shift is induced on two-single-photon input states, and thus a quantum gate build from such a medium cannot work. Here we show that a fast response Kerr medium induces some but very little phase shifts on a two-single-photon input state, and it is insufficient for high fidelity quantum computation. We point out that this is caused by the medium imparting spectral entanglement to the input photons. We further show that a way to circumvent this problem and achieve a high fidelity gate, is to engineer the dispersion properties of the medium to give a dominant spectral effect over the non-instantaneous response, in addition to satisfying a phase matching condition.

arXiv:0810.2828•Oct 16, 2008•3 citations

Cross-Kerr nonlinearity between continuous-mode coherent states and single photons

Bing He, Qing Lin, Christoph Simon

Weak cross-Kerr nonlinearities between single photons and coherent states are the basis for many applications in quantum-information processing. These nonlinearities have so far mainly been discussed in terms of highly idealized single-mode models. We develop a general theory of the interaction between continuous-mode photonic pulses and apply it to the case of a single photon interacting with a coherent state. We quantitatively study the validity of the usual single-mode approximation using the concepts of fidelity and conditional phase. We show that high fidelities, nonzero conditional phases, and high photon numbers are compatible, under conditions where the pulses fully pass through each other and where unwanted transverse-mode effects are suppressed.

arXiv:1102.3724•Physical Review A•May 18, 2011•114 citations

Memory-enhanced noiseless cross-phase modulation

Mahdi Hosseini, S. Rebić, Ben M. Sparkes +3 more

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.

arXiv:1112.2010•Light Science & Applications•Dec 7, 2012•58 citations
Abstract. The weak nonlinear Kerr interaction between single photons and intense laser fields has been recently proposed as a basis for distributed optics-based solutions to few-qubit applications in quantum communication and computation. Here, we analyze the above Kerr interaction by employing a continuous-time multi-mode model for the input/output fields to/from the nonlinear medium. In contrast to previous single-mode treatments of this problem, our analysis takes into account the full temporal content of the free-field input beams as well as the non-instantaneous response of the medium. The main implication of this model, in which the cross-Kerr phase shift on one input is proportional to the photon flux of the other input, is the existence of phase noise terms at the output. We show that these phase noise terms will degrade the performance of the parity gate proposed by Munro, Nemoto, and Spiller [1].Continuous-time cross-phase modulation and quantum computation 2 1.
The weak nonlinear Kerr interaction between single photons and intense laser fields has been recently proposed as a basis for distributed optics-based solutions to few-qubit applications in quantum communication and computation. Here, we analyse the above Kerr interaction by employing a continuous-time multi-mode model for the input/output fields to/from the nonlinear medium. In contrast to previous single-mode treatments of this problem, our analysis takes into account the full temporal content of the free-field input beams as well as the non-instantaneous response of the medium. The main implication of this model, in which the cross-Kerr phase shift on one input is proportional to the photon flux of the other input, is the existence of phase noise terms at the output. We show that these phase noise terms will preclude satisfactory performance of the parity gate proposed by Munro et al (2005 New J. Phys. 7 137).
A cross-Kerr interaction produces a phase shift on two modes of light proportional to the number of photons in both modes and is sometimes called cross-phase modulation. Cross-Kerr nonlinearities have many applications in classical and quantum nonlinear optics, including the possibility of a deterministic and all-optical controlled-phase gate. We calculate the one- and two-photon SSS matrices for fields propagating in a medium where the cross-Kerr interaction is spatially distributed at discrete interaction sites comprised of atoms. For the interactions considered, we analyze the cases where the photons copropagate and counterpropagate through the medium and give a physical interpretation to the differences between the two cases. Finally, we obtain the SSS matrix in the limit of infinitely long chains, showing that it corresponds to a perfect controlled-phase operation.
According to idealized models, a strong Kerr non-linearity may be used to build optical quantum gates for optical quantum information processing by inducing conditional phase shifts on quantum states. Recently, Shapiro (PRA 73, 062305 (2006)) argued that for a Kerr medium with non-instantaneous but fast response, essentially no phase shift is induced on two-single-photon input states, and thus a quantum gate build from such a medium cannot work. Here we show that a fast response Kerr medium induces some but very little phase shifts on a two-single-photon input state, and it is insufficient for high fidelity quantum computation. We point out that this is caused by the medium imparting spectral entanglement to the input photons. We further show that a way to circumvent this problem and achieve a high fidelity gate, is to engineer the dispersion properties of the medium to give a dominant spectral effect over the non-instantaneous response, in addition to satisfying a phase matching condition.
Weak cross-Kerr nonlinearities between single photons and coherent states are the basis for many applications in quantum-information processing. These nonlinearities have so far mainly been discussed in terms of highly idealized single-mode models. We develop a general theory of the interaction between continuous-mode photonic pulses and apply it to the case of a single photon interacting with a coherent state. We quantitatively study the validity of the usual single-mode approximation using the concepts of fidelity and conditional phase. We show that high fidelities, nonzero conditional phases, and high photon numbers are compatible, under conditions where the pulses fully pass through each other and where unwanted transverse-mode effects are suppressed.
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.