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arXiv:2003.10519 · Physical review. D/Physical review. D.

Heisenberg limit for detecting vacuum birefringence

Naser Ahmadiniaz, T. E. Cowan, Roland A. Sauerbrey, Ulrich Schramm, Hans-Peter Schlenvoigt, Ralf Schützhold

Published Jun 30, 2020• 20 citations
arXivHTMLPDF

Abstract

Quantum electrodynamics predicts the vacuum to behave as a nonlinear medium, including effects such as birefringence. However, for experimentally available field strengths, this vacuum polarizability is extremely small and thus very hard to measure. In analogy to the Heisenberg limit in quantum metrology, we study the minimum requirements for such a detection in a given strong field (the pump field). Using a laser pulse as the probe field, we find that its energy must exceed a certain threshold depending on the interaction time. However, a detection at that threshold, i.e., the Heisenberg limit, requires highly nonlinear measurement schemes---while for ordinary linear-optics schemes, the required energy (Poisson or shot noise limit) is much larger. Finally, we discuss several currently considered experimental scenarios from this point of view.

DOI
10.1103/physrevd.101.116019

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Quantum electrodynamics predicts the vacuum to behave as a nonlinear medium, including effects such as birefringence. However, for experimentally available field strengths, this vacuum polarizability is extremely small and thus very hard to measure. In analogy to the Heisenberg limit in quantum metrology, we study the minimum requirements for such a detection in a given strong field (the pump field). Using a laser pulse as the probe field, we find that its energy must exceed a certain threshold depending on the interaction time. However, a detection at that threshold, i.e., the Heisenberg limit, requires highly nonlinear measurement schemes---while for ordinary linear-optics schemes, the required energy (Poisson or shot noise limit) is much larger. Finally, we discuss several currently considered experimental scenarios from this point of view.
Quantum Electrodynamics predicts that the vacuum must behave as a nonlinear optical medium: the vacuum optical index should increase when it is stressed by intense electromagnetic fields. The DeLLight (Deflection of Light by Light) project aims to measure it by using intense and ultra-short laser pulses. The experiment uses a Sagnac interferometer to amplify the tiny deflection signal of a low-intensity probe pulse crossing the vacuum refractive-index gradient produced by an external high-intensity pump pulse. The measurement of the amplified signal by a CCD camera requires a high spatial resolution, which is limited by the ultimate quantum noise of the CCD. However, interferometric phase noise induced by the mechanical vibrations of the interferometer is also amplified and degrades spatial resolution. To overcome this, we propose a new method named High-Frequency Phase Noise Suppression (HFPNS), based on the addition of a delayed replica (5 ns) of the probe pulse. The delayed pulse, which is not affected by the pump but is subject to the same vibration noise, enables offline subtraction of correlated phase noise. In this work, we present an experimental proof-of-concept on a prototype interferometer operating with a limited amplification factor (A≃25\mathcal{A}\simeq25A≃25), about 10 times smaller than the required value of the final experiment. We have succeeded in reducing phase noise by a factor of 40, resulting in a residual noise level 2.3 times higher than the expected quantum noise. The residual noise is linked to delay-line instabilities and incident beam pointing fluctuations present during these tests. This result validates HFPNS as a robust method for future quantum-noise-limited interferometric measurements of vacuum optical nonlinearity, though additional stabilization and higher interferometric amplification are still needed.
Quantum interferometric sensing plays a crucial role in a wide range of applications, including quantum metrology, quantum imaging, and quantum lithography, where minute phase shifts carry valuable physical information. The strength of quantum sensing lies in surpassing classical sensitivity limits, particularly through the use of quantum correlations and squeezing to suppress optical shot noise. Birefringence sensing is crucial for various applications, as it provides detailed information about the material's structure, stress, composition, and environmental conditions. We present an interferometric scheme for detecting unknown small birefringence beyond the shot-noise limit of sensitivity that leverages the hyper-squeezing (squeezed in both number-phase and polarization correlations) within a pair of polarized nonlinear SU(1,1) interferometers, coupled by the birefringence. Specifically, two pairs of crossed-polarization nonlinear media, both generate and measure two-mode quantum light that is squeezed and polarization-entangled. We present a complete theoretical analysis of the interferometer's sensitivity to small birefringence under realistic conditions of gain and internal loss, illuminating the potential for enhancement of the sensitivity by 3-15dB in practical, real-world experiments (the exact achievable enhancement is governed solely by the loss).
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The ultimate precision of phase estimation is limited by the Heisenberg scaling Δϕ0=K/NΔϕ_0 = K/NΔϕ0​=K/N, where K∼1K\sim1K∼1 is a numerical prefactor and NNN is the mean number of photons interacting with the phase shifting object(s). However, achieving this fundamental limit often comes at the cost of an extremely narrow high-sensitive range, rendering schemes impractical. We analyze the precision limits of phase measurements in single- and two-arm optical interferometers with input Gaussian states. We consider two detection methods: conventional homodyne measurement and non-Gaussian threshold detection that saturates the quantum Cramér-Rao bound. We characterize the performance by two complementary metrics: the peak sensitivity Δϕ0Δϕ_0Δϕ0​ and the width δϕδϕδϕ of the high-sensitivity range. We demonstrate that Heisenberg scaling is attainable in all configurations considered. However, we reveal that δϕδϕδϕ strongly depends on KKK. We derive an approximate analytic expression that describes this trade-off. We show also that the two-arm interferometer with antisymmetrically squeezed inputs exhibits exceptional performance, simultaneously achieving Heisenberg-limited sensitivity and a broad high-sensitivity range δϕ=π/2δϕ=π/2δϕ=π/2.
The Heisenberg limit is the superior precision available by entanglement sensors. However, entanglementis fragile against dephasing, and there is no known quantum metrology protocol that can achieve Heisenberg limited sensitivity with the presence of independent dephasing. Here, we show that the Heisenberg limit is attainable under the effect of independent dephasing under conditions where the probe qubits decohere due to both target fields and local environments. To detect the target fields, we exploit the entanglement properties to decay much faster than the classical states due to collective noise while most of the previous schemes use a coherent phase shift from the target fields. Actually, if the temporally fluctuating target fields behave as Markovian collective dephasing, we can estimate the collective dephasing rate with a sensitivity at the Heisenberg limit under the effect of independent dephasing. Our work opens the possibility for robust Heisenberg-limited metrology.
The fields of quantum and nonlinear optics have given rise to a variety of nonclassical states of light that have been proven to surpass certain limitations set by classical physics. Namely, certain squeezed and entangled states have been shown to beat the shot-noise limit when making precision phase measurements in interferometry, as well as write lithographic patterns that are smaller than classically allowed by the Rayleigh diffraction limit. Additionally, single-photon sources and entangled photon pairs have given rise to provably secure quantum key distribution for cryptography. Producing these quantum states of light has proven a difficult task. Nonlinear crystals, when pumped by a laser, produce pairs of single photons via the process of spontaneous parametric down conversion (SPDC). This process is mediated by the second order nonlinear susceptibility of the material. When pumped in a high gain regime, these crystals give rise to optical parametric amplification, which is a viable source of squeezed light. The vast majority of research in this area has focused on crystals that are seeded by vacuum in their two modes. This dissertation concerns the field of quantum nonlinear optics. It is an investigation into the processes that occur when nonlinear materials interact with the electromagnetic field on the single photon level. I have focused on seeding nonlinear crystals with quantum states of light, including single photons and entangled states. This process results in various states directly applicable to interferometry, imaging, and cryptography. Another application investigated is an absolute radiance measurement via stimulated parametric down conversion resulting from non-vacuum seeding of a nonlinear crystal. Additionally, other nonlinear processes, including four-wave mixing, nonlinear magneto-optical effects and coherent population trapping in warm atomic vapor involving quantum states of light are investigated. The process of seeding third-order nonlinear interactions, such as in atomic vapors, gives rise to a variety of interesting, nonclassical phenomena such as entangled image transfer and nonlocal imaging. Strong analogies between SPDC and four-wave mixing are drawn. I also experimentally show an all optical pi-only phase shift of one light beam via another in warm Cesium vapor.