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arXiv:1007.3256 · Optics Express

Modal and polarization qubits in Ti:LiNbO_3 photonic circuits for a universal quantum logic gate

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

Published Sep 10, 2010• 25 citations
arXivHTMLPDF

Abstract

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).

DOI
10.1364/oe.18.020475

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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).
On-chip integrated photonic circuits are crucial for further progress toward quantum technologies and in the science of quantum optics. The quantum controlled-Z gate is an example of the maximally entangling gate, which is universal for quantum computing when coupled with single-qubit gates. This article demonstrates a deterministic controlled-Z photonic quantum gate based on titanium in-diffused channel waveguides in which polarization and modal degrees of freedom of a single photon are used for encoding the control and target qubits, respectively.
The ability to manipulate quantum states of light by integrated devices may open new perspectives both for fundamental tests of quantum mechanics and for novel technological applications. However, the technology for handling polarization-encoded qubits, the most commonly adopted approach, is still missing in quantum optical circuits. Here we demonstrate the first integrated photonic controlled-NOT (CNOT) gate for polarization-encoded qubits. This result has been enabled by the integration, based on femtosecond laser waveguide writing, of partially polarizing beam splitters on a glass chip. We characterize the logical truth table of the quantum gate demonstrating its high fidelity to the expected one. In addition, we show the ability of this gate to transform separable states into entangled ones and vice versa. Finally, the full accessibility of our device is exploited to carry out a complete characterization of the CNOT gate through a quantum process tomography. As quantum information processing continues to develop apace, the need for integrated photonic devices becomes ever greater for both fundamental measurements and technological applications. To this end, Crespiet al.demonstrate a high-fidelity photonic controlled-NOT gate on a glass chip.
We report on the theoretical design and simulation of a photonic quantum circuit that operates as a single-photon, two-qubit swap gate. In this approach, the circuit is implemented in Titanium indiffused LiNbO3 channel waveguides, and polarization and spatial encoding are utilized to realize the qubits. A set of basic components comprising a dual periodically poled waveguide for two simultaneous Type-0 and Type-I non-linear interactions, as well as the passive routing and active electro-optically controllable devices, are the main building blocks in this circuit. Simulations are carried out by making use of the numerical beam propagation method incorporated within RSoft program package.
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.