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arXiv:1704.01964 · Scientific Reports

Duality and quantum state engineering in cavity arrays

Nilakantha Meher, S. Sivakumar, Prasanta Kumar Panigrahi

Published Aug 17, 2017• 20 citations
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Abstract

A system of two coupled cavities with N - 1 photons is shown to be dynamically equivalent to an array of N coupled cavities containing one photon. Every transition in the two cavity system has a dual phenomenon in terms of photon transport in the cavity array. This duality is employed to arrive at the required coupling strengths and nonlinearities in the cavity array so that controlled photon transfer is possible between any two cavities. This transfer of photons between two of the cavities in the array is effected without populating the other cavities. The condition for perfect transport enables perfect state transfer between any two cavities in the array. Further, possibility of high fidelity generation of generalized NOON states in two coupled cavities, which are dual to the Bell states of the photon in the cavity array, is established.

DOI
10.1038/s41598-017-08569-8

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A system of two coupled cavities with N - 1 photons is shown to be dynamically equivalent to an array of N coupled cavities containing one photon. Every transition in the two cavity system has a dual phenomenon in terms of photon transport in the cavity array. This duality is employed to arrive at the required coupling strengths and nonlinearities in the cavity array so that controlled photon transfer is possible between any two cavities. This transfer of photons between two of the cavities in the array is effected without populating the other cavities. The condition for perfect transport enables perfect state transfer between any two cavities in the array. Further, possibility of high fidelity generation of generalized NOON states in two coupled cavities, which are dual to the Bell states of the photon in the cavity array, is established.
We demonstrate a scheme for quantum communication between the ends of an array of coupled cavities. Each cavity is doped with a single two level system (atoms or quantum dots) and the detuning of the atomic level spacing and photonic frequency is appropriately tuned to achieve photon blockade in the array. We show that in such a regime, the array can simulate a dual rail quantum state transfer protocol where the arrival of quantum information at the receiving cavity is heralded through a fluorescence measurement. Communication is also possible between any pair of cavities of a network of connected cavities.
We study the photon transfer along a linear array of three coupled cavities where the central one contains an interacting two-level system in the strong- and ultrastrong-coupling regimes. We find that an inhomogeneously coupled array forbids a complete single-photon transfer between the external cavities when the central one performs a Jaynes-Cummings dynamics. This is not the case in the ultrastrong-coupling regime, where the system exhibits singularities in the photon transfer time as a function of the cavity-qubit coupling strength. Our model can be implemented within the state-of-the-art circuit quantum electrodynamics technology and it represents a building block for studying photon state transfer through scalable cavity arrays.
We demonstrate a scheme for quantum communication between the ends of an array of coupled cavities. Each cavity is doped with a single two level system (atoms or quantum dots) and the detuning of the atomic level spacing and photonic frequency is appropriately tuned to achieve photon blockade in the array. We show that in such a regime, the array can simulate a dual rail quantum state transfer protocol where the arrival of quantum information at the receiving cavity is heralded through a fluorescence measurement. Communication is also possible between any pair of cavities of a network of connected cavities.
We theoretically study how to control transport, bound states, and resonant states of a single photon in a one-dimensional coupled-cavity array. We find that the transport of a single photon in the cavity array can be controlled by tuning the frequency of either one or two cavities. If one of the cavities in the array has a tunable frequency, and its frequency is tuned to be larger (or smaller) than those of other cavities, then there is a photon bound state above (or below) the energy band of the coupled-cavity array. However, if two cavities in the array have tunable frequencies, then there exist both bound states and resonant states. If the frequencies of the two cavities are chosen to be much larger than those of other cavities, and the hopping couplings between any two nearest-neighbor cavities are weak, then a single photon with a resonant wave vector can be trapped in the region between the two frequency-tunable cavities. In this case, a quantum supercavity can be formed by these two frequency-tunable cavities. We also study how to apply this photon transport control to an array of coupled superconducting transmission line resonators.
We propose a quantum state transfer (QST) scheme that transfers any single-mode photon state along a one-dimensional coupled-cavity array (CCA). By building a map from QST in a CCA to that in a spin- 1 2 chain, we show that many previous results of QST schemes for the spin chain system find similar applications in the CCA system. Furthermore, high fidelity QST along a long CCA can be achieved for arbitrary initial states. Using numerical simulations we provide a visual presentation of the result: at some time τ the CCA system gets high fidelity QST under different initial conditions. Finally we discuss possible experimental realizations of our QST scheme.
The problem of the complete transfer of quantum states and entanglement in a four-qubit system composed of two single-mode cavities and two two-level atoms is investigated. The transfer of single and double excitation states is discussed for two different coupling configurations between the qubits. In the first, the coupling is mediated by the atoms that simultaneously couple to the cavity modes. In the second configuration, each atom resides inside one of the cavities and the coupling between the cavities is mediated by the overlapping field modes. A proper choice of basis states makes it possible to identify states that could be completely transferred between themselves. Simple expressions are derived for the conditions for the complete transfer of quantum states and entanglement. These conditions impose severe constraints on the evolution of the system in the form of constants of motion. The constrains on the evolution of the system imply that not all states can evolve in time, and we find that the evolution of the entire system can be confined into that occurring among two states only. Detailed analysis show that in the case where the interaction is mediated by the atoms, only symmetric superposition states can be completely and reversibly transferred between the atoms and the cavity modes. In the case where the interaction is mediated by the overlapping field modes, both symmetric and antisymmetric superposition states can be completely transferred. We also show that the system is capable of generating purely photonic NOON states, but only if the coupling is mediated by the atoms, and demonstrate that the ability to generate the NOON states relies on perfect transfer of an entanglement from the atoms to the cavity modes.