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arXiv:1007.3242 · IEEE photonics journal

Photonic Circuits for Generating Modal, Spectral, and Polarization Entanglement

Mohammed F. Saleh, Giovanni Di Giuseppe, Bahaa E. A. Saleh, Malvin Carl Teich

Published Aug 5, 2010• 33 citations
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Abstract

We consider the design of photonic circuits that make use of Ti:LiNbO3diffused channel waveguides to generate photons with various combinations of modal, spectral, and polarization entanglement. Down-converted photon pairs are generated via spontaneous parametric down-conversion (SPDC) in a two-mode waveguide (TMW). We study a class of photonic circuits comprising: 1) a nonlinear periodically poled TMW structure; 2) a set of single-mode waveguide (SMW)- and TMW-based couplers arranged in such a way that they suitably separate the three photons comprising the SPDC process; and, for some applications, 3) a holographic Bragg grating that acts as a dichroic reflector. The first circuit produces two frequency-degenerate down-converted photons, each with even spatial parity, in two separate SMWs. Changing the parameters of the elements allows this same circuit to produce two nondegenerate down-converted photons that are entangled in frequency or simultaneously entangled in frequency and polarization. The second photonic circuit is designed to produce modal entanglement by distinguishing the photons on the basis of their frequencies. A modified version of this circuit can be used to generate photons that are doubly entangled in mode number and polarization. The third photonic circuit is designed to manage dispersion by converting modal, spectral, and polarization entanglement into path entanglement.

DOI
10.1109/jphot.2010.2062494

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We consider the design of photonic circuits that make use of Ti:LiNbO3diffused channel waveguides to generate photons with various combinations of modal, spectral, and polarization entanglement. Down-converted photon pairs are generated via spontaneous parametric down-conversion (SPDC) in a two-mode waveguide (TMW). We study a class of photonic circuits comprising: 1) a nonlinear periodically poled TMW structure; 2) a set of single-mode waveguide (SMW)- and TMW-based couplers arranged in such a way that they suitably separate the three photons comprising the SPDC process; and, for some applications, 3) a holographic Bragg grating that acts as a dichroic reflector. The first circuit produces two frequency-degenerate down-converted photons, each with even spatial parity, in two separate SMWs. Changing the parameters of the elements allows this same circuit to produce two nondegenerate down-converted photons that are entangled in frequency or simultaneously entangled in frequency and polarization. The second photonic circuit is designed to produce modal entanglement by distinguishing the photons on the basis of their frequencies. A modified version of this circuit can be used to generate photons that are doubly entangled in mode number and polarization. The third photonic circuit is designed to manage dispersion by converting modal, spectral, and polarization entanglement into path entanglement.
We examine the modal, spectral, and polarization entanglement properties of photon pairs generated in a nonlinear periodically poled two-mode waveguide (one-dimensional planar or two-dimensional circular) via nondegenerate spontaneous parametric down-conversion. Any of the possible degrees of freedom---mode number, frequency, or polarization---can be used to distinguish the down-converted photons while the others serve as attributes of entanglement. Distinguishing the down-converted photons based on their mode numbers enables us to efficiently generate spectral or polarization entanglement that is either narrowband or broadband. On the other hand, when the generated photons are distinguished by their frequencies in a type-0 process, modal entanglement turns out to be an efficient alternative to polarization entanglement. Moreover, modal entanglement in type-II down-conversion may be used to generate a doubly entangled state in frequency and polarization.
In this paper, we propose a method for the generation of higher dimensional modal entanglement through type II spontaneous parametric down conversion process using a three waveguide directional coupler in a periodically poled lithium niobate substrate. We show that by a proper design, it is possible to achieve an output state of two photons occupying three different spatial modes. The advantage of using such waveguide structure is its flexibility and the design space availability to achieve desired characteristics of the photon pairs generated in the down conversion process
In this paper, we propose a method for the generation of higher-dimensional modal entanglement through a type II spontaneous parametric down-conversion process using a three-waveguide directional coupler in a periodically poled lithium niobate substrate. We show that by a proper design, it is possible to achieve an output state of two photons occupying three different spatial modes. The advantage of using such waveguide structure is its flexibility and the design space availability to achieve desired characteristics of the photon pairs generated in the down-conversion process.
Integrated optical devices are expected to play a promising role in the field of quantum information science and technology. In this paper we propose a scheme for the generation of nondegenerate, copolarized, modal, and path-entangled photons using a directional coupler and an asymmetric Y\mathsf{Y}Y-coupler geometry in type-0 phase-matched domain-engineered lithium niobate (LN) waveguide. The nonlinearity in LN is tailored in such a way that quasi-phase-matching conditions for two different spontaneous parametric down-conversion processes are obeyed simultaneously, leading to a modal and path-entangled state at the output. Assuming typical values of various parameters, we show, through numerical simulations, that an almost maximally entangled state is achievable over a wide range of waveguide parameters. For the degenerate case, the proposed scheme gives a NOON state for NNN === 2. The generated entangled photon pairs should have potential applications in quantum information schemes and also in quantum metrology. By appropriate domain engineering and component designing, the idea can be further extended to generate hyperentangled and two-photon multipath-entangled states, which may have further applications in quantum computation protocols.
Lithium niobate photonic circuits have the salutary property of permitting the generation, transmission, and processing of photons to be accommodated on a single chip. Compact photonic circuits such as these, with multiple components integrated on a single chip, are crucial for efficiently implementing quantum information processing schemes.We present a set of basic transformations that are useful for manipulating modal qubits in Ti:LiNbO(3) photonic quantum circuits. These include the mode analyzer, a device that separates the even and odd components of a state into two separate spatial paths; the mode rotator, which rotates the state by an angle in mode space; and modal Pauli spin operators that effect related operations. We also describe the design of a deterministic, two-qubit, single-photon, CNOT gate, a key element in certain sets of universal quantum logic gates. It is implemented as a Ti:LiNbO(3) photonic quantum circuit in which the polarization and mode number of a single photon serve as the control and target qubits, respectively. It is shown that the effects of dispersion in the CNOT circuit can be mitigated by augmenting it with an additional path. The performance of all of these components are confirmed by numerical simulations. The implementation of these transformations relies on selective and controllable power coupling among single- and two-mode waveguides, as well as the polarization sensitivity of the Pockels coefficients in LiNbO(3).