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Optica

Electro-optic interface for ultrasensitive intracavity electric field measurements at microwave and terahertz frequencies

Ileana-Cristina Benea-Chelmus, Yannick Salamin, Francesca Fabiana Settembrini, Yuriy Myronovych Fedoryshyn, Wolfgang Heni, Delwin L. Elder, Larry R. Dalton, Juerg Leuthold, Jérôme Faist

Published Apr 20, 2020• 66 citations
Publisher

Abstract

Electro-optic quantum coherent interfaces map the amplitude and phase of a quantum signal directly to the phase or intensity of a probe beam. At terahertz frequencies, a fundamental challenge is not only to sense such weak signals (due to a weak coupling with a probe in the near-infrared) but also to resolve them in the time domain. Cavity confinement of both light fields can increase the interaction and achieve strong coupling. Using this approach, current realizations are limited to low microwave frequencies. Alternatively, in bulk crystals, electro-optic sampling was shown to reach quantum-level sensitivity of terahertz waves. Yet, the coupling strength was extremely weak. Here, we propose an on-chip architecture that concomitantly provides subcycle temporal resolution and an extreme sensitivity to sense terahertz intracavity fields below 20 V/m. We use guided femtosecond pulses in the near-infrared and a confinement of the terahertz wave to a volume of V T H z ∼ 10 − 9 ( λ T H z / 2 ) 3 in combination with ultraperformant organic molecules ( r 33 = 170 p m / V ) and accomplish a record-high single-photon electro-optic coupling rate of g e o = 2 π × 0.043 G H z , 10,000 times higher than in recent reports of sensing vacuum field fluctuations in bulk media. Via homodyne detection implemented directly on chip, the interaction results into an intensity modulation of the femtosecond pulses. The single-photon cooperativity is C 0 = 1.6 × 10 − 8 , and the multiphoton cooperativity is C = 0.002 at room temperature. We show > 70 d B dynamic range in intensity at 500 ms integration under irradiation with a weak coherent terahertz field. Similar devices could be employed in future measurements of quantum states in the terahertz at the standard quantum limit, or for entanglement of subsystems on subcycle temporal scales, such as terahertz and near-infrared quantum bits.

DOI
10.1364/optica.384160

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Electro-optic quantum coherent interfaces map the amplitude and phase of a quantum signal directly to the phase or intensity of a probe beam. At terahertz frequencies, a fundamental challenge is not only to sense such weak signals (due to a weak coupling with a probe in the near-infrared) but also to resolve them in the time domain. Cavity confinement of both light fields can increase the interaction and achieve strong coupling. Using this approach, current realizations are limited to low microwave frequencies. Alternatively, in bulk crystals, electro-optic sampling was shown to reach quantum-level sensitivity of terahertz waves. Yet, the coupling strength was extremely weak. Here, we propose an on-chip architecture that concomitantly provides subcycle temporal resolution and an extreme sensitivity to sense terahertz intracavity fields below 20 V/m. We use guided femtosecond pulses in the near-infrared and a confinement of the terahertz wave to a volume of V T H z ∼ 10 − 9 ( λ T H z / 2 ) 3 in combination with ultraperformant organic molecules ( r 33 = 170 p m / V ) and accomplish a record-high single-photon electro-optic coupling rate of g e o = 2 π × 0.043 G H z , 10,000 times higher than in recent reports of sensing vacuum field fluctuations in bulk media. Via homodyne detection implemented directly on chip, the interaction results into an intensity modulation of the femtosecond pulses. The single-photon cooperativity is C 0 = 1.6 × 10 − 8 , and the multiphoton cooperativity is C = 0.002 at room temperature. We show > 70 d B dynamic range in intensity at 500 ms integration under irradiation with a weak coherent terahertz field. Similar devices could be employed in future measurements of quantum states in the terahertz at the standard quantum limit, or for entanglement of subsystems on subcycle temporal scales, such as terahertz and near-infrared quantum bits.
The metrology of terahertz waves is a prerequisite for future applications in communications, sensing or spectroscopy. Electro-optic transduction, the technique by which a terahertz signal is mapped onto an optical or near-infrared signal, has emerged as one of the most sensitive metrology techniques that also provides sub-picosecond temporal resolution. As such, it has been employed to detect quantum terahertz fields for the first time. Recent advances in the miniaturization of these transducers target increased sensitivities, a small footprint and compatibility with large photonic architectures. In this talk, I will outline the basics of electric field metrology at the quantum limit and discuss how integrated photonics could open entirely new avenues in the area of spatially and temporally multiplexed terahertz detection.
A time-domain approach to quantum electrodynamics is presented, covering the entire mid-infrared and terahertz frequency ranges. Ultrabroadband electro-optic sampling with few-femtosecond laser pulses allows direct detection of the vacuum fluctuations of the electric field in free space [1,2]. Besides the Planck and electric field fundamental constants, the variance of the ground state is determined solely by the inverse of the four-dimensional space-time volume over which a measurement or physical process integrates. Therefore, we can vary the contribution of multi-terahertz vacuum fluctuations and discriminate against the trivial shot noise due to the constant flux of near-infrared probe photons. Subcycle temporal resolution based on a nonlinear phase shift provides signals from purely virtual photons for accessing the ground-state wave function without amplification to finite intensity. Recently, we have succeeded in generation and analysis of mid-infrared squeezed transients with quantum noise patterns that are time-locked to the intensity envelope of the probe pulses. We find subcycle temporal positions with a noise level distinctly below the bare vacuum which serves as a direct reference. Delay times with increased differential noise indicate generation of highly correlated quantum fields by spontaneous parametric fluorescence. Our time-domain approach offers a generalized understanding of spontaneous emission processes as a consequence of local anomalies in the co-propagating reference frame modulating the quantum vacuum, in combination with the boundary conditions set by Heisenberg’s uncertainty principle. [1] C. Riek et al., Science 350, 420 (2015) [2] A. S. Moskalenko et al., Phys. Rev. Lett. 115, 263601 (2015)
The manipulation of visible and near-infrared light at the single-photon level plays a key role in quantum communication systems where information is encoded into photonic degrees of freedom. In practical implementations, it is important to achieve this manipulation with high speeds, low loss, and low noise. In this Letter, we propose the use of terahertz electric fields as a pump source for electro-optic modulation of single photons in bulk media. We demonstrate spectral modulations of single photons in the form of frequency translation and bandwidth manipulations as the terahertz field imparts linear and quadratic phases on the photons at various time delays within 1 ps. Our results show frequency translations exceeding 500 GHz at multi-THz modulation speeds and loss levels of ≈1 dB, complementing the current state-of-the-art electro-optic modulation techniques limited to speeds up to 100 GHz. The proposed approach leverages recent developments in terahertz generation techniques, introducing new avenues to manipulate nonclassical light in an unexplored regime for quantum photonics.
Electro-optical sampling of Terahertz fields with ultrashort pulsed probes is a well-established approach for directly measuring the electric field of THz radiation. This technique usually relies on balanced detection to record the optical phase shift brought by THz-induced birefringence. The sensitivity of electro-optical sampling is, therefore, limited by the shot noise of the probe pulse, and improvements could be achieved using quantum metrology approaches using, e.g., NOON states for Heisenberg-limited phase estimation. We report on our experiments on THz electro-optical sampling using single-photon detectors and a weak squeezed vacuum field as the optical probe. Our approach achieves field sensitivity limited by the probe state statistical properties using phase-locked single-photon detectors and paves the way for further studies targeting quantum-enhanced THz sensing.
Abstract In recent years, electro-optic sampling, which is based on Pockel’s effect between an electromagnetic mode and a copropagating, phase-matched ultrashort probe, has been largely used for the investigation of broadband quantum states of light, especially in the mid-infrared and terahertz frequency range. The use of two mutually delayed femtosecond pulses at near-infrared frequencies allows the measurement of quantum electromagnetic radiation in different space-time points. Their correlation allows therefore direct access to the spectral content of a broadband quantum state at terahertz frequencies after Fourier transformation. In this work, we will prove experimentally and theoretically that when using strongly focused coherent ultrashort probes, the electro-optic sampling technique can be affected by the presence of a third-order nonlinear mixing of the probes’ electric field at near-infrared frequencies. Moreover, we will show that these third-order nonlinear phenomena can also influence correlation measurements of the quantum electromagnetic radiation. We will prove that the four-wave mixing of the coherent probes’ electric field with their own electromagnetic vacuum at near-infrared frequencies results in the generation of a higher-order nonlinear correlation term. The latter will be characterized experimentally, proving its local nature requiring the physical overlap of the two probes. The parameters regime where higher order nonlinear correlation results predominant with respect to electro-optic correlation of terahertz radiation is provided.
Direct detection of vacuum fluctuations and analysis of subcycle quantum properties of the electric field are explored by a paraxial quantum theory of ultrafast electro-optic sampling. The feasibility of such experiments is demonstrated by realistic calculations adopting a thin ZnTe electro-optic crystal and stable few-femtosecond laser pulses. We show that nonlinear mixing of a short near-infrared probe pulse with the multiterahertz vacuum field leads to an increase of the signal variance with respect to the shot noise level. The vacuum contribution increases significantly for appropriate length of the nonlinear crystal, short pulse duration, tight focusing, and a sufficiently large number of photons per probe pulse. If the vacuum input is squeezed, the signal variance depends on the probe delay. Temporal positions with a noise level below the pure vacuum may be traced with subcycle resolution.