Nonlocal dispersion cancellation for three or more photons

I. C. Nodurft, S. U. Shringarpure, B. T. Kirby, T. B. Pittman, and J. D. Franson

Phys. Rev. A 102, 013713 – Published 14 July 2020

Abstract

The entanglement of quantum systems can produce a variety of nonclassical effects that have practical applications in quantum information science. One example of this is nonlocal dispersion cancellation, in which the effects of dispersion on one photon can be canceled out by the dispersion experienced by a second photon at a distant location. In this paper, we extend the analysis of nonlocal dispersion cancellation to three or more photons. We find that energy-time entanglement of three or more photons can lead to a complete or partial cancellation of dispersion depending on the experimental conditions. These results may be useful in implementing quantum key distribution in networks with three or more nodes.

Received 30 March 2020
Accepted 16 June 2020

DOI:https://doi.org/10.1103/PhysRevA.102.013713

Physics Subject Headings (PhySH)

Photon pairs & parametric down-conversion Quantum communication Quantum fluctuations & noise Quantum optics Quantum states of light

Atomic, Molecular & OpticalQuantum Information, Science & Technology

Authors & Affiliations

I. C. Nodurft¹, S. U. Shringarpure ¹, B. T. Kirby², T. B. Pittman¹, and J. D. Franson¹

¹Physics Department, University of Maryland, Baltimore County, Baltimore, Maryland 21250, USA
²Army Research Laboratory, Adelphi, Maryland 20783, USA

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 102, Iss. 1 — July 2020

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
An entangled three-photon source using a $χ^{(3)}$ nonlinear crystal pumped by a laser at a frequency of $ω_{0}$ . Each photon passes through a filter with bandwidth $σ_{F}$ before propagating through separate media with dispersion coefficients given by $β_{1}, β_{2}$ , and $β_{3}$ .
Reuse & Permissions
Figure 2
The same entangled three-photon source shown in Fig. 1, with the addition of a narrow-band filter and detector placed in the path of photon 3. This allows postselection on the frequency of photon 3.
Reuse & Permissions
Figure 3
Probability distribution that detectors 2 and 3 will detect a single photon with a time lag of $t$ and $t + τ$ (dimensionless) after detector 1, respectively, for a relatively narrow-band filter with $σ_{F} = 0.10$ (arbitrary units). Panels (a,b) correspond to the quantum-mechanical and classical results, respectively, for no dispersion $(β_{1} = β_{2} = β_{3} = 0)$ . The quantum and classical results are shown in (c,d) for a set of parameters with $ω_{0} = 1, β_{1} x_{1} = 100, β_{2} x_{2} = - 50$ , and $β_{3} x_{3} = - 50$ . Panels (e,f) correspond to $β_{1} x_{1} = 200, β_{2} x_{2} = - 100$ , and $β_{3} x_{3} = - 100$ . It can be seen that the timing uncertainties are significantly smaller for the quantum-mechanical results in (c,e) due to nonlocal cancellation of dispersion.
Reuse & Permissions
Figure 4
Probability distribution that detectors 2 and 3 will detect a single photon with a time lag of $t$ and $t + τ$ (dimensionless) after detector 1, respectively, for a broader filter bandwidth $(σ_{F} = 0.50)$ than in Fig. 3 (arbitrary units). The quantum-mechanical results are once again shown on the left-hand side while the corresponding classical results are on the right. Panels (a,b) correspond to no dispersion as before, while (c,d) correspond to $ω_{0} = 1, β_{1} x_{1} = 12.5, β_{2} x_{2} = - 25$ , and $β_{3} x_{3} = - 37.5$ . Panels (e,f) correspond to $β_{1} x_{1} = 50, β_{2} x_{2} = - 100$ , and $β_{3} x_{3} = - 150$ . The differences between the quantum-mechanical and classical results are more pronounced for a wider filter bandwidth.
Reuse & Permissions
Figure 5
Comparison of the analytic and numerical calculations of the quantum-mechanical timing probability distribution as a function of the time delays $t$ and $τ$ (dimensionless). (a) Analytic calculations using the narrow-band-filter approximation. (b) Exact results from a numerical calculation. Both of these results correspond to the same parameters as in Fig. 4. It can be seen that the width is somewhat larger in the numerical results but it is still much smaller than the corresponding classical results in Fig. 4.
Reuse & Permissions

Physical Review A

covering atomic, molecular, and optical physics and quantum information