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State Engineering via Nonlinear Interferometry with Linear Spectral Phases

Cody Charles Payne, Elaganuru Bashaiah, Markus Allgaier

TL;DR

This work addresses spectral-state engineering in SPDC to enable high-dimensional spectral qudits and entangled states. It introduces a nonlinear interferometer with four crystals and linear spectral-phase control to generate grid states or high-dimensional entangled states by selecting time-delay sequences, and analyzes the effect of loss on state purity and interference visibility. Key contributions include explicit modulation functions for grid and HDE states, simulation results for ppKTP and ppLNO3 implementations, and a loss-analysis showing differential robustness of grid versus HDE states. The approach provides a versatile, component-based route to spectral multiplexing and quantum information protocols with potential practical implementations.

Abstract

Many protocols within quantum cryptography, communications, and computing require the ability to generate entangled states as well as spectral qudits. Nonlinear interferometry is a viable way to engineer these complex quantum states of light. However, it is difficult to achieve a high level of control over spectral correlations. Here, we present a protocol utilizing a nonlinear interferometer with linear spectral phases that can generate both high-dimensional spectral qudits and high-dimensional entangled states. We model the effect of loss and loss of overlap on interference visibility and thereby on the states generated.

State Engineering via Nonlinear Interferometry with Linear Spectral Phases

TL;DR

This work addresses spectral-state engineering in SPDC to enable high-dimensional spectral qudits and entangled states. It introduces a nonlinear interferometer with four crystals and linear spectral-phase control to generate grid states or high-dimensional entangled states by selecting time-delay sequences, and analyzes the effect of loss on state purity and interference visibility. Key contributions include explicit modulation functions for grid and HDE states, simulation results for ppKTP and ppLNO3 implementations, and a loss-analysis showing differential robustness of grid versus HDE states. The approach provides a versatile, component-based route to spectral multiplexing and quantum information protocols with potential practical implementations.

Abstract

Many protocols within quantum cryptography, communications, and computing require the ability to generate entangled states as well as spectral qudits. Nonlinear interferometry is a viable way to engineer these complex quantum states of light. However, it is difficult to achieve a high level of control over spectral correlations. Here, we present a protocol utilizing a nonlinear interferometer with linear spectral phases that can generate both high-dimensional spectral qudits and high-dimensional entangled states. We model the effect of loss and loss of overlap on interference visibility and thereby on the states generated.
Paper Structure (9 sections, 38 equations, 7 figures)

This paper contains 9 sections, 38 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Theory
  3. Nonlinear Interferometer Scheme
  4. Scheme for Generating Grid State
  5. Scheme for Generating High-Dimensional Entangled State
  6. Simulation Results
  7. Analysis of Loss
  8. Discussion and Conclusion
  9. Derivation of the modulation functions

Figures (7)

  • Figure 1: Block diagram of the nonlinear interferometer apparatus for generating the grid state. The fundamental time delay is $\tau=8.3\,\mathrm{ps}$. This is only a simplified version of the apparatus, not depicting actual optical components in the laboratory. Note that the pump (violet beam) does transmit through the final crystal, but we show it terminating there as a simplistic illustration of the fact that we filter it out at the end to leave only signal and idler beams at the final fiber couplings.
  • Figure 2: Block diagram of the nonlinear interferometer apparatus for generating the high-dimensional entangled state. The fundamental time delay is $\tau=1.0\,\mathrm{ps}$.
  • Figure 3: The joint spectral grid states along with the pump, phase matching, and modulation functions and the projected idler photon state. (a) The norm-square of the pump envelope function for the grid state. (b) The norm-square of the phase matching function for the grid state. (c) The unmodulated joint spectral intensity for the grid state. (d) The norm square of the modulation function for the grid state displayed with pseudo-normalization. (e) The grid state . (f) The norm-square of the grid state where projective measurement projects onto $\lambda_s=1550\,\text{nm}$.
  • Figure 4: The HDE joint spectrum. (a) Norm square of the pump envelope function for the HDE state. (b) Norm square of the phase matching function for the HDE state. (c) The unmodulated joint spectral intensity for the HDE state. (d) Modulation function for the HDE state. (e) The modulated joint spectral intensity HDE state.
  • Figure 5: The results of numerical analysis of the behavior of the Schmidt number as a function of loss (blue line), overlap of the lossy state with the lossless state vs. loss (solid magenta line), and overlap of the lossy state with the unmodulated state (dashed magenta lines) for the grid state (a) and HDE state (b).
  • ...and 2 more figures