IEEE Lasers and Electro-Optics Society Annual Meeting (LEOS)
Terahertz Quantum Optics in the Time-Domain: From Field Correlation Measurements on Vacuum Field Fluctuations in Free Space towards Cavity Electro-Optics
Ileana-Crsitina Benea-Chelmus, Francesca Fabiana Settembrini, Yannick Salamin, Yuriy Myronovych Fedoryshyn, Wolfgang Heni, Delwin L. Elder, Larry R. Dalton, Juerg Leuthold, Giacomo Scalari, Jérôme Faist
The ground state of electromagnetic radiation is characterised by a fluctuating electromagnetic field even in a vacuum. We measure its correlation function as a function of time and space using the electro-optic effect. We determine the spectral content and the amplitude of this state and find excellent agreement with the second quatisation theory. Finally, we discuss the potential of recent electro-optic quantum coherent interfaces for cavity electrodynamics experiments in the terahertz.
The ground state of electromagnetic radiation is characterised by a fluctuating electromagnetic field even in a vacuum. We measure its correlation function as a function of time and space using the electro-optic effect. We determine the spectral content and the amplitude of this state and find excellent agreement with the second quatisation theory. Finally, we discuss the potential of recent electro-optic quantum coherent interfaces for cavity electrodynamics experiments in the terahertz.
The ground state of quantum systems is characterized by zero-point motion. This motion, in the form of vacuum fluctuations, is generally considered to be an elusive phenomenon that manifests itself only indirectly. Here, we report direct detection of the vacuum fluctuations of electromagnetic radiation in free space. The ground-state electric-field variance is inversely proportional to the four-dimensional space-time volume, which we sampled electro-optically with tightly focused laser pulses lasting a few femtoseconds. Subcycle temporal readout and nonlinear coupling far from resonance provide signals from purely virtual photons without amplification. Our findings enable an extreme time-domain approach to quantum physics, with nondestructive access to the quantum state of light. Operating at multiterahertz frequencies, such techniques might also allow time-resolved studies of intrinsic fluctuations of elementary excitations in condensed matter.
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 fascinating nature of light has driven many discoveries in physics, from the theory of special relativity to quantum mechanics. As a carrier of information, light is at the core of high-speed communication over the internet and facilitates the study of numerous physical properties of materials by the interaction of light and matter. Advances in generating and detecting ultrashort light pulses enabled the spectroscopic investigation of matter with unprecedented detail. Meanwhile, the development of more precise and sensitive measurements, leveraging quantum properties of light, has expanded the experimental frontiers of the physical world. Naturally, the question arises: Could the combination of these two breakthroughs push the frontiers even further? A promising candidate to achieve this combination is electro-optic sampling, an electromagnetic-field measurement comprising an up-conversion and a phase-space measurement based on homodyne detection. While it is predominantly used in classical terahertz time-domain spectroscopy, the high sensitivity and spatio-temporal resolution of electro-optic sampling recently enabled the detection of vacuum fluctuations in the ground state of the electromagnetic field by probing an adjustable space-time volume. Yet, the generation and characterization of more intricate quantum pulses on ultrafast timescales is still challenging, especially in the terahertz frequencies. Exploiting the quantum properties of a light pulse over a broad frequency range requires sophisticated knowledge about the prepared quantum pulse as well as the measurement setup at use. However, Heisenberg's uncertainty relation fundamentally prevents the complete determination of an arbitrary quantum state from a single measurement. Instead, the quantum state has to be reconstructed from the statistics of many measurements — a process known as quantum state tomography. In this thesis, we establish the theoretical foundations for a comprehensive tomographic reconstruction of pulsed quantum states of light, encompassing both the statistics and dynamics of the state. Additionally, we introduce tools to simplify the description of the nonlinear interaction underlying electro-optic sampling and in turn the tomography setups presented here. As a first step, we investigate the application of electro-optic sampling to the time-local reconstruction of various pulsed quantum states of light on ultrafast timescales. We identify two types of noise, which impact the quality of the reconstruction: shot noise, arising from the nonlinear interaction in electro-optic sampling, and thermal noise, due to the localization of the (correlated) quantum state within a small space-time volume during the measurement. To improve the reconstruction, we propose to use a strong probe pulse, suppressing the shot noise, and to select an appropriate detection frequency band, reducing thermal noise. Thus, the proposed tomography enables the characterization of quantum states in terahertz frequency range on ultrafast timescales. However, the time-local nature of the measurement imposes a trade-off between the reconstruction of the quantum state in phase space and the time domain. In a second step, we propose a reconstruction method based on two-time field-correlation measurement, which we call correlation tomography, able to overcome the restriction to time-local states. While the tomography of quantum states in an optimal pulse basis has been demonstrated, it requires prior knowledge about the temporal structure of the quantum state. We introduce an algorithm for reconstructing high-dimensional multimode Gaussian quantum states, which are completely characterized by the covariance matrix of the quadratures of fully distinguishable pulses. The reconstruction is achieved by orthogonalizing the overlapping time windows of the correlation measurement in post-processing. We compare a homodyne-based implementation to electro-optic sampling and develop an optimization scheme for the latter, to mitigate the shot noise in the non-perturbative regime of strong nonlinear interactions. Furthermore, we derive the full-counting statistics of the field-correlation measurement and theoretically demonstrate the reconstruction of pulsed Fock states. This opens an avenue to the full tomography of highly multimode non-Gaussian states. In the third and last step, we derive a formalism to simplify the description of the up-conversion required in electro-optic sampling. If a pulsed quantum states is up-converted and localized in a small space-time region, the transformation of the localized modes during the nonlinear interaction corresponds to an open quantum system, rendering the standard tools of quantum optics inapplicable. By introducing the generalized Bloch-Messiah decomposition, we simplify the input-output relation of the nonlinear interaction to a set of effective modes relevant for subsequent processing, such as detection. Using this framework, we derive an analytic phase-space input-output relation for the nonlinear interaction of pulsed quantum states, applicable to open quantum systems. We study the resulting dynamics using two example input states: a Fock state and a two-mode squeezed state. Based on the von Neumann entropy of the output state, we develop an intuitive understanding of the generalized Bloch-Messiah decomposition. The rich structure of pulsed quantum states of light can be a powerful resource, but also challenging to operate with, in theory as well as in experiment. The characterization methods and theoretical tools developed in this thesis, tailored to pulsed quantum light and the nonlinear interaction thereof, can pave the way to the application of this resource to fundamental research as well as quantum technologies.
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 correlation of the quantum-mechanical ground-state fluctuations of the electric-field strength in a dispersive and lossy linear dielectric are studied in terms of the symmetrized autocorrelation function, with special emphasis on the optical frequency domain. Starting from the canonical quantization scheme developed by Huttner and Barnett [Phys. Rev. A 46, 4306 (1992)], the analysis is based on a quantization of the phenomenological Maxwell theory, the effect of the medium being described by a frequency-dependent complex permittivity. In this way, the spectrally resolved ground-state autocorrelation function of the electric-field strength can be expressed in terms of the real and imaginary parts of the refractive index. Both analytical and numerical results are presented and the effects of dispersion and absorption including their dependence on the frequency interval chosen are discussed. A comparison with the vacuum fluctuations in free space is given.
In many states of the quantum electromagnetic field, including the vacuum state, entanglement exists between different space-time regions---even spacelike separated ones. These correlations can be harvested and, thereby, detected by quantum systems which locally interact with the field. Here, we propose an experimental implementation of such an entanglement-harvesting scheme which is based on electro-optic sampling (EOS). We demonstrate that state-of-the-art EOS experiments enable one to harvest entanglement from the vacuum field and to study quantum correlations within general THz fields. We further show how Bell nonlocality present in the vacuum field can be probed. Finally, we introduce an approach to mitigate shot noise in single-beam EOS configurations. These findings pave the way for experimental inquiries into foundational properties of relativistic quantum field theory, and empower EOS as a diagnostic tool in THz quantum optics.