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Journal of the Optical Society of America B

Dynamics of a Schrödinger cat state in a photonic waveguide array

Dante Urbieta Maldonado, J. S. S. Durán Gómez, Roberto Ramírez-Alarcón, Laura E. C. Rosales-Zárate

Published Dec 3, 2024• 2 citations
Publisher

Abstract

We report the study of the dynamics of a Schrödinger cat state (SCS) in a photonic lattice, in which two different types of coupling functions between the waveguides are considered: a constant coupling and a parabolic coupling. In addition, we investigate the inclusion of defects in the constant coupling function condition for one or three waveguides. In our study, we evaluate the average number of photons per waveguide and the fidelity in order to determine the distribution of light in the lattice for each coupling function and to find conditions to reach a perfect state transfer (PST). In the case of constant coupling, it is not possible to obtain a PST since the state distributes over all the lattice, with the inclusion of defects serving as a control mechanism in this process. In the case of parabolic coupling, we observe PST when the lattice is composed of an odd number of coupled waveguides, while, for an even number of coupled waveguides, we observe that by varying the phase of the SCS, different values of the fidelity can be obtained. Interestingly, in this last case, it is possible to achieve values of the fidelity closer to one by choosing a phase of π and a small average number of photons.

DOI
10.1364/josab.542282

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We report the study of the dynamics of a Schrödinger cat state (SCS) in a photonic lattice, in which two different types of coupling functions between the waveguides are considered: a constant coupling and a parabolic coupling. In addition, we investigate the inclusion of defects in the constant coupling function condition for one or three waveguides. In our study, we evaluate the average number of photons per waveguide and the fidelity in order to determine the distribution of light in the lattice for each coupling function and to find conditions to reach a perfect state transfer (PST). In the case of constant coupling, it is not possible to obtain a PST since the state distributes over all the lattice, with the inclusion of defects serving as a control mechanism in this process. In the case of parabolic coupling, we observe PST when the lattice is composed of an odd number of coupled waveguides, while, for an even number of coupled waveguides, we observe that by varying the phase of the SCS, different values of the fidelity can be obtained. Interestingly, in this last case, it is possible to achieve values of the fidelity closer to one by choosing a phase of π and a small average number of photons.
Abstract We report the study of non-classical light in a photonic lattice having a parabolic coupling distribution, also known as a J x photonic lattice. We focus on a two-photon Fock state, a two-photon N 00 N state, a single-mode squeezed state and a coherent state as inputs to the lattice. We investigate the possibility of a perfect transfer of the mean photon number as well as the quantum state from one waveguide mode to another. We study photon–photon correlation for the two-photon N 00 N state. For the single-mode squeezed state we perform a detailed study of the evolution of the squeezing factor and entanglement between the waveguide modes. Our findings suggest a perfect transfer of the average photon number in all cases and a perfect transfer of the quantum state in the cases of the two-photon Fock state and the two-photon N 00 N state only, but not in the cases of the squeezed and coherent states. Our results should have applications in the physical implementation of photonic continuous-variable quantum-information processing.
We propose a quantum network consisting of optical waveguides in the linear regime for quantum state transfer. The circular topology of our network introduces novel functionalities that enable us to analytically identify the conditions under which perfect state transfer (PST) is achievable. We utilize the properties of the Fourier modes, in particular the zero Fourier modes, which provide a protected subspace for the efficient propagation of quantum states, resulting in PST to the diametrically opposite site in a network with any number of sites N=4nN = 4nN=4n. The coupling profiles in the photonic network modulate the number of zero-energy eigenmodes, with uniform couplings yielding more than evanescent ones, confirming that the expedition of observed PST originates from the collapse of the eigenvalue spectrum into three distinct eigenvalue blocks, including N/2N/2N/2 manifolds of zero Fourier modes. We investigate PST in both discrete- and continuous-variable input regimes, using single photon state, Schrödinger cat states, and two-mode squeezed vacuum state. Our findings apply to the engineering of quantum networks and photonic lattices, paving the way for applications in controlled routing in integrated quantum circuits.
We report the study of non-classical light in a photonic lattice having parabolic coupling distribution, also known as Jx photonic lattice. We focus on two photon Fock state, two photon N00N state, and single mode squeezed state along with coherent state as input to the lattice. We investigate the possibility of perfect transfer of mean photon number as well as quantum state from one waveguide mode to other. We study photon-photon correlation for two photon N00N state. For single mode squeezed state we study in detail, the evolution of squeezing factor and entanglement between the waveguide modes. Our findings suggest perfect transfer of average photon number for all cases and perfect transfer of quantum state in case of two photon Fock state and two photon N00N state only and not in the case of squeezed and coherent state. Our results should have applications in physical implementation of photonic continuous variable quantum information processing.
We study the quantum correlation of path-entangled states of two photons in coupled one-dimensional waveguide arrays with lattice defects. Both off-diagonal and diagonal defects are considered, which show different effects on the quantum correlation of path-entangled two-photon states. Two-photon bunching or anti-bunching effects can be observed and controlled. The two photons are found to have a tendency to bunch at the side lobes with a repulsive off-diagonal defect, and the path-entanglement of the input two-photon state can be preserved during the propagation. We also found that defect modes may play an important role on the two-photon correlation of path-entangled states in the waveguide arrays. Due to the quantum interference effect, intriguing evolution dynamics of the two-photon correlation matrix elements with oscillation frequencies being either twice of or the same as that of a classical light wave, depending on the position of the correlation matrix element, is observed. Our results show that it is possible to manipulate the two-photon correlation properties of path-entangled states in waveguide arrays with lattice defects.
In quantum optics, photonic Schrödinger cats are superpositions of two coherent states with opposite phases and with a significant number of photons. Recently, these states have been observed in the transient dynamics of driven-dissipative resonators subject to engineered two-photon processes. Here we present an exact analytical solution of the steady-state density matrix for this class of systems, including one-photon losses, which are considered detrimental for the achievement of cat states. We demonstrate that the unique steady state is a statistical mixture of two cat-like states with opposite parity, in spite of significant one-photon losses. The transient dynamics to the steady state depends dramatically on the initial state and can pass through a metastable regime lasting orders of magnitudes longer than the photon lifetime. By considering individual quantum trajectories in photon-counting configuration, we find that the system intermittently jumps between two cats. Finally, we propose and study a feedback protocol based on this behaviour to generate a pure cat-like steady state.
Taking the decoherence into account, we investigate nonclassical features of the optical Schr\"odinger cat states in one-mode and two-coupled-modes systems with two-photon driving. In the one-mode system, the relationship between the Schr\"odinger cat states and the system parameters is derived. We observe that in the presence of single-photon decay the steady states would be a mixture of Schr\"odinger cat states. The dynamics and steady states of such a cat versus single-photon decay are examined. In the two-coupled-modes cases with linear and nonlinear couplings, the dynamics of entanglement and mutual information are examined with two different initial states and single-photon decay. Compared to the linear coupling case, more complicated structure appears in the Wigner function in the nonlinear coupling case. The joint quadrature distributions are also explored. Such nonclassical states can be used not only in exploring the boundary between the classical and the quantum worlds but also in quantum metrology and quantum information processing.