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

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:LiNbO3 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:LiNbO3 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 LiNbO3.

Modelling of Output Statistics of Single and -Mode Straight and Curved :Ti:LiNb Waveguide Amplifiers

“…In Figures 3 and 4 the spectral dependences of the Fano factor (3) and the statistical fluctuation (4) in single pass configuration are presented.…”

“…This is the reason why, over the last decade, a great attention has been devoted to the analysis of the statistical properties of Er 3+ -doped fibres and waveguide amplifiers [1][2][3][4][5][6][7][8][9][10][11][12].…”

Mode analyzer and modal phase-flip gate for integrated photonic circuits

“…It represents a coherent superposition of the basis states, generally denoted 0 and 1 [9][10]. A qubit can be encoded in any of several degrees-of-freedom of a single photon, such as polarization [5], spatial parity [11], or the mode number of a single photon confined to a two-mode waveguide [12][13]. Indeed, polarization offers an intrinsically binary basis and is often used to realize a qubit.…”

“…Recently, silica waveguide circuits on silicon chips have been employed in quantum applications to realize stable interferometers for two-qubit entangling gates [2,4]. For these materials, however, the photon-generation process necessarily lies off-chip [2,5]. Lithium niobate photonic circuits have the distinct advantage that they permit the generation, transmission, and processing of photons all to be achieved on a single chip [5][6].…”

“…Lithium niobate photonic circuits have the distinct advantage that they permit the generation, transmission, and processing of photons all to be achieved on a single chip [5][6]. Moreover, lithium niobate offers a number of ancillary advantages: its properties are well-understood [5,7]; circuit elements, such as two-mode waveguides and polarization-sensitive mode-separation structures, have low loss [5]; it exhibits an electro-optic effect that can modify the refractive index at rates up to tens of GHz and is polarization-sensitive [5,8]; and periodic poling of the second order nonlinear optical coefficient is straightforward so that phase-matched parametric interactions , such as SPDC and the generation of entangled-photon pairs, can be readily achieved [5][6]. This paper describes two building blocks useful for manipulating modal qubits in Ti:LiNbO3 photonic quantum circuits.…”