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Development of Biphoton Entangled Light Spectroscopy (BELS) using Bell pairs

V. V. Desai, N. P. Armitage

Abstract

We introduce Biphoton Entanglement Light Spectroscopy (BELS), a quantum spectroscopic technique that employs polarization entangled Bell pairs and two photon interference to probe material properties. In BELS, the measured signal arises not from single photon intensities but from changes in the joint polarization and path correlations of biphoton Bell pairs transmitted through or scattered by a sample and analyzed via cross channel coincidences. A key concept of BELS is the explicit mapping between Jones matrix operations and transformations within the Bell state manifold. Optical elements that are equivalent under classical polarization optics can produce qualitatively distinct signatures in the coincidence landscape when interrogated with entangled photons. We demonstrate that linear birefringence and Faraday rotation generate orthogonal admixtures of Bell states, yielding experimentally distinguishable coincidence channels within a single measurement. We measure birefringence in an anisotropic dielectric and Faraday rotation in $\text{Tb}_3\text{Ga}_5\text{O}_{12}$. By mapping the changes to the photonic entanglement, BELS establishes a new framework for future entanglement enhanced spectroscopy, a potentially powerful approach in characterizing quantum materials, nanophotonic devices, and light matter interactions perhaps eventually at a fundamentally quantum level.

Development of Biphoton Entangled Light Spectroscopy (BELS) using Bell pairs

Abstract

We introduce Biphoton Entanglement Light Spectroscopy (BELS), a quantum spectroscopic technique that employs polarization entangled Bell pairs and two photon interference to probe material properties. In BELS, the measured signal arises not from single photon intensities but from changes in the joint polarization and path correlations of biphoton Bell pairs transmitted through or scattered by a sample and analyzed via cross channel coincidences. A key concept of BELS is the explicit mapping between Jones matrix operations and transformations within the Bell state manifold. Optical elements that are equivalent under classical polarization optics can produce qualitatively distinct signatures in the coincidence landscape when interrogated with entangled photons. We demonstrate that linear birefringence and Faraday rotation generate orthogonal admixtures of Bell states, yielding experimentally distinguishable coincidence channels within a single measurement. We measure birefringence in an anisotropic dielectric and Faraday rotation in . By mapping the changes to the photonic entanglement, BELS establishes a new framework for future entanglement enhanced spectroscopy, a potentially powerful approach in characterizing quantum materials, nanophotonic devices, and light matter interactions perhaps eventually at a fundamentally quantum level.
Paper Structure (6 sections, 11 equations, 6 figures)

This paper contains 6 sections, 11 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Results
  3. Discussion
  4. Methods
  5. Acknowledgments
  6. Author Contributions

Figures (6)

  • Figure 1: Modified Hong–Ou–Mandel Interferometer for Biphoton Entanglement Light Spectroscopy (BELS). The scheme incorporates entangled Bell pairs and polarization detection. HWP - half wave plate, BP - birefringent plate, BBO - $\beta$-Barium Borate, LB - Laser beam Block, S- sample, IF - Interference filter, CS - Collimation system, BS- 50/50 beamsplitter, PBS - polarizing beam splitter. In arm $b$ a dielectric compensator (fused silica or a HWP) was introduced to match the optical thickness of the sample placed in arm $a$ (not shown).
  • Figure 2: Polarization-Resolved HOM Interference for a Nominal $| \Phi^+ \rangle$ State. Coincidences as a function of relative arm delay for coincidence channels for a nominal $| \Phi^+ \rangle$ input state for a pair of 3mm orthogonally attached BBO crystals for Type I SPDC. (a) $\mathrm{H}_{\mathrm{c}}$:$\mathrm{H}_{\mathrm{d}}.$ (b) $\mathrm{V}_{\mathrm{c}}$:$\mathrm{H}_{\mathrm{d}}.$ (c) $\mathrm{H}_{\mathrm{c}}$:$\mathrm{V}_{\mathrm{c}}.$ (d) $\mathrm{V}_{\mathrm{c}}$:$\mathrm{V}_{\mathrm{d}}$. Note that vastly different scales of (a) and (d) as compared to (b) and (c) Fits are Gaussian plus a constant.
  • Figure 3: Biphoton Coherence as a function of relative delay with Coincidence Landscapes. Coincidences for channels $\mathrm{H}_{\mathrm{c}}$:$\mathrm{H}_{\mathrm{d}}$ (Minima; 124, Plateau; 5806), $\mathrm{V}_{\mathrm{c}}$:$\mathrm{H}_{\mathrm{d}}$ (Minima; 159, Plateau; 228) , $\mathrm{H}_{\mathrm{c}}$:$\mathrm{V}_{\mathrm{c}}$ (Maxima; 393, Plateau; 282), $\mathrm{V}_{\mathrm{c}}$:$\mathrm{V}_{\mathrm{d}}$ (Minima; 98, Plateau; 5425 ) for Type I SPDC for a pair of 0.5 mm BBO crystals and a 30 nm interference filter. Fits are Gaussian plus a constant.
  • Figure 4: Birefringence-Induced Transformations within the Bell-State Manifold. Scan of 4 coincidences at the zero relative delay position as a function of rotation of a HWP placed in the optical path $a$. Solid lines are fits to the form $\sin^{2}(2\theta)$ with an offset. $\mathrm{H}_{\mathrm{c}}$:$\mathrm{H}_{\mathrm{d}}$ (0$^\circ$; 783, 45$^\circ$; 34), $\mathrm{V}_{\mathrm{c}}$:$\mathrm{H}_{\mathrm{d}}$ (0$^\circ$; 175, 45$^\circ$; 2103) , $\mathrm{H}_{\mathrm{c}}$:$\mathrm{V}_{\mathrm{c}}$ (0$^\circ$; 191, 45$^\circ$; 11129), $\mathrm{V}_{\mathrm{c}}$:$\mathrm{V}_{\mathrm{d}}$ (0$^\circ$; 2058, 45$^\circ$; 48 )
  • Figure 5: Magnetic-Field-Induced Admixture of $|\Psi^{-}\rangle$ in Tb$_3$Ga$_5$O$_{12}$.$\mathrm{V}_{\mathrm{c}}$:$\mathrm{H}_{\mathrm{d}}$ coincidence counts as a function of relative delay for different applied magnetic fields for a 10 mm thick TGG sample placed in beam path $a$. Solid line are fits to Gaussian with an offset. We believe the gradual horizontal shift is due to mechanical flexure of the sample stage in magnetic field.
  • ...and 1 more figures