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Physical Review A

Quantum logic operations based on photon-exchange interactions

J. D. Franson, T. B. Pittman

Published Aug 1, 1999• 27 citations
Publisher

Abstract

Nonlinear interactions between two photons are required for the construction of optical quantum logic gates, but those interactions are normally very weak due to the small magnitude of the electric field associated with a single photon. We note that exchange interactions can have a large effect even when there is no physical interaction between two particles, and we exploit this property for the construction of optical quantum logic gates. We show that the probability of there being two virtually-excited atoms in a medium can be a factor of 2 larger when two nonresonant photons propagate through the same medium as compared to the case in which they propagate through two separate media, in analogy with photon bunching. As a result, the application of one or more laser pulses will produce a nonlinear phase shift that can be used to construct an XOR quantum logic gate. This provides an example of a quantum control process in which one photon can control the state of another photon even when there is no sequence of physical interactions linking the two photons. From a classical point of view, it is not possible to identify a path for the flow of information or a specific cause for the outcome of the control process.

DOI
10.1103/physreva.60.917

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Quantum logic gates using photon exchange interactions

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Summary form only given. Nonlinear interactions between two photons are normally very weak because of the weak electric field associated with a single photon. We recently suggested that this difficulty could be avoided by relying on exchange interactions, which can have large effects even when there is no physical interaction at all between two particles. We consider two photons in well collimated beams that are incident upon an atomic vapor cell. The probability of there being two excited atoms in the medium is shown to be a factor of two larger in that case than if the two photons were incident upon two separate but otherwise identical media.

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Nonlinear interactions between two photons would have many potential applications, including the implementation of quantum logic gates for use in quantum computing. We are investigating a new mechanism for nonlinear optics at the two-photon level that is based on the exchange of photons by pairs of atoms in a medium, such as an atomic vapor. The effect can be understood as being due to a factor of two increase in the probability of having two excited atoms in the medium compared to the case in which the two photons propagate in two separate media. These effects are expected to be sufficiently large that cavities and traps should not be required, which may eventually allow the construction of large numbers of simple quantum logic gates. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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The operation of a quantum computer is inherently nonlocal due to the entanglement of separated quantum gates. This paper is concerned instead with the use of nonlocal effects to construct the quantum gates themselves. A nonlocal interaction in which pairs of atoms exchange two photons is expected to produce a large nonlinear phase shift. An interesting feature of this effect is that energy is not conserved at the location of an individual atom but it is conserved overall. The preliminary results from a series of experiments in a sodium vapor cell are in apparent agreement with the predictions of the theory. These nonlinear phase shifts can be used to construct quantum logic gates, such as a Controlled-NOT.

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•Nov 6, 2019•0 citations
Nonlinear interactions between two photons are required for the construction of optical quantum logic gates, but those interactions are normally very weak due to the small magnitude of the electric field associated with a single photon. We note that exchange interactions can have a large effect even when there is no physical interaction between two particles, and we exploit this property for the construction of optical quantum logic gates. We show that the probability of there being two virtually-excited atoms in a medium can be a factor of 2 larger when two nonresonant photons propagate through the same medium as compared to the case in which they propagate through two separate media, in analogy with photon bunching. As a result, the application of one or more laser pulses will produce a nonlinear phase shift that can be used to construct an XOR quantum logic gate. This provides an example of a quantum control process in which one photon can control the state of another photon even when there is no sequence of physical interactions linking the two photons. From a classical point of view, it is not possible to identify a path for the flow of information or a specific cause for the outcome of the control process.
Summary form only given. Nonlinear interactions between two photons are normally very weak because of the weak electric field associated with a single photon. We recently suggested that this difficulty could be avoided by relying on exchange interactions, which can have large effects even when there is no physical interaction at all between two particles. We consider two photons in well collimated beams that are incident upon an atomic vapor cell. The probability of there being two excited atoms in the medium is shown to be a factor of two larger in that case than if the two photons were incident upon two separate but otherwise identical media.
Nonlinear interactions between two photons would have many potential applications, including the implementation of quantum logic gates for use in quantum computing. We are investigating a new mechanism for nonlinear optics at the two-photon level that is based on the exchange of photons by pairs of atoms in a medium, such as an atomic vapor. The effect can be understood as being due to a factor of two increase in the probability of having two excited atoms in the medium compared to the case in which the two photons propagate in two separate media. These effects are expected to be sufficiently large that cavities and traps should not be required, which may eventually allow the construction of large numbers of simple quantum logic gates. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
The operation of a quantum computer is inherently nonlocal due to the entanglement of separated quantum gates. This paper is concerned instead with the use of nonlocal effects to construct the quantum gates themselves. A nonlocal interaction in which pairs of atoms exchange two photons is expected to produce a large nonlinear phase shift. An interesting feature of this effect is that energy is not conserved at the location of an individual atom but it is conserved overall. The preliminary results from a series of experiments in a sodium vapor cell are in apparent agreement with the predictions of the theory. These nonlinear phase shifts can be used to construct quantum logic gates, such as a Controlled-NOT.
In this dissertation, we shall focus on theoretically studying quantum nonlinear optical schemes to construct a conditional phase gate at the single-photon level. With an aim to develop analytical models, we shall carry out a rigorous quantized multimode field analysis of some of these schemes involving only the interacting field operators. More specifically, we shall first study the three-wave mixing process involving two single-photons in a second-order nonlinear medium (x(2)) under two different cases viz. when the photons are traveling with equal velocities and when they are traveling with different velocities, and explore the possibility of using them for building a conditional phase phase gate. Finally, we shall study the interaction of single-photon wavepackets with a realistic atomic system viz. an ensemble of five-level atoms, to construct a phase gate. We will particularly look at the "giant Kerr" effect in electromagnetically induced transparency to explore the possibility of using this scheme for achieving a conditional phase shift and to understand how the bandwidth gets restricted naturally in such an atomic system.
Photon-based quantum logic gate has substantial advantages over conventional atom-based designs as a result of a longer coherence time and an inherent compatibility with quantum communication protocol of flying qubits, photons. As a vital logic gate for universal quantum computing, the two-photon controlled-phase gate demands a few-photon nonlinearity, which historically suffers from either an indeterministic nature in the linear optics regime, or a weak nonlinearity within naturally-occurring materials in the nonlinear optics regime. It is intriguing yet challenging to deliver a logic gate design by exploiting a genuine fewphoton nonlinearity. In this dissertation, we study a particular one-dimensional quantum nanophotonic system that offers the desired few-photon nonlinearity through light-matter interactions in the quantum limit (i.e., between light quanta of photons and individual material formation of atoms). Towards this end, we study the exotic photonic trimer state generation to frst demonstrate few-photon nonlinearity. Then we report the breakdown of the non-Hermitian Hamiltonian for correlated multi-photon process to unveil the non-trivial effects of few-photon nonlinearity. Finally by exploiting such a nonlinearity, we present a deterministic two-photon controlled-phase gate proposal, and further showcase universal quantum logic gate designs in quantum nanophotonic systems.