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arXiv:1901.06749 · Ultrafast Phenomena and Nanophotonics

Terahertz strong-field physics without a strong external terahertz field

Motoaki Bamba, Xinwei Li, Junichiro Kono

Published Feb 27, 2019• 5 citations
arXivHTMLPDF

Abstract

Traditionally, strong-field physics explores phenomena in laser-driven matter (atoms, molecules, and solids) that cannot be understood by treating the laser field as a small perturbation. Therefore, the presence of an extremely strong external field is usually a prerequisite for observing strong-field phenomena. However, even in the complete absence of an external electromagnetic field, strong-field phenomena can arise when matter strongly couples with the zero-point field of the quantum vacuum state, i.e., fluctuating electromagnetic waves whose expectation value is zero. This can occur in free space where the matter strongly interacts with a continuum of photon modes, but some of the most striking examples of strong-field physics without an external field occur in a cavity setting, in which an ensemble of two-level atoms resonantly interacts with a single photonic mode of vacuum fields, producing vacuum Rabi splitting. In particular, the nature of the matter-vacuum-field coupled system fundamentally changes when the coupling rate (equal to one half of the vacuum Rabi splitting) becomes comparable to, or larger than, the resonance frequency. In this so-called ultrastrong coupling regime, a non-negligible number of photons exist in the ground state of the coupled system. Furthermore, the coupling rate can be cooperatively enhanced (via so-called Dicke cooperativity) when the matter is comprised of a large number of identical two-level particles, and a quantum phase transition is predicted to occur as the coupling rate reaches a critical value. Low-energy electronic or magnetic transitions in many-body condensed matter systems with large dipole moments are ideally suited for searching for these predicted phenomena. Here, we discuss two condensed matter systems that have shown cooperative ultrastrong interactions in the terahertz frequency range: a Landau-quantized two-dimensional electron gas interacting with high-quality-factor cavity photons, and an Er3+ spin ensemble interacting with Fe3+ magnons in ErFeO3.

DOI
10.1117/12.2512794

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Dressing quantum states of matter with virtual photons can create exotic effects ranging from vacuum-field modified transport to polaritonic chemistry, and may drive strong squeezing or entanglement of light and matter modes. The established paradigm of cavity quantum electrodynamics focuses on resonant light-matter interaction to maximize the coupling strength ΩR/ωcΩ_\mathrm{R}/ω_\mathrm{c}ΩR​/ωc​, defined as the ratio of the vacuum Rabi frequency and the carrier frequency of light. Yet, the finite oscillator strength of a single electronic excitation sets a natural limit to ΩR/ωcΩ_\mathrm{R}/ω_\mathrm{c}ΩR​/ωc​. Here, we demonstrate a new regime of record-strong light-matter interaction which exploits the cooperative dipole moments of multiple, highly non-resonant magnetoplasmon modes specifically tailored by our metasurface. This multi-mode coupling creates an ultrabroadband spectrum of over 20 polaritons spanning 6 optical octaves, vacuum ground state populations exceeding 1 virtual excitation quantum for electronic and optical modes, and record coupling strengths equivalent to ΩR/ωc=3.19Ω_\mathrm{R}/ω_\mathrm{c}=3.19ΩR​/ωc​=3.19. The extreme interaction drives strongly subcycle exchange of vacuum energy between multiple bosonic modes akin to high-order nonlinearities otherwise reserved to strong-field physics, and entangles previously orthogonal electronic excitations solely via vacuum fluctuations of the common cavity mode. This offers avenues towards tailoring phase transitions by coupling otherwise non-interacting modes, merely by shaping the dielectric environment.
Dressing electrons with the vacuum electromagnetic field of an optical microresonator can lead to the creation of new states of matter. When the rate of energy exchange between the two systems, the vacuum Rabi frequency, Ω R , becomes comparable to the carrier frequency of light, ω 0 , the regime of ultrastrong coupling is reached [1] . Here, anti-resonant interactions result in a modified vacuum ground state and give rise to novel phenomena of cavity quantum electrodynamics (c-QED), such as the vacuum Bloch-Siegert shift [2] . When Ω R even surpasses ω 0 , deepstrong coupling is attained [3] , [4] . While the exploration of the equilibrium properties of this extreme setting has just begun, its subcycle dynamics is expected to reveal qualitatively new quantum phenomena.
Strong coupling of light and matter is an essential element of cavity quantum electrodynamics (cavity-QED) and quantum optics, which may lead to novel mixed states of light and matter and to applications such as quantum computation. In the strong-coupling regime, where the coupling strength exceeds the dissipation, the light-matter interaction produces a characteristic vacuum Rabi splitting. Therefore, strong coupling can be utilized as an effective coherent interface between light and matter (in the form of electron charge, spin or superconducting Cooper pairs) to achieve components of quantum information technology including quantum memory, teleportation, and quantum repeaters. Semiconductor quantum dots, nuclear spins and paramagnetic spin systems are only some of the material systems under investigation for strong coupling in solid-state physics. Mixed states of light and matter coupled via electric dipole transitions often suffer from short coherence times (nanoseconds). Even though magnetic transitions appear to be intrinsically more quantum coherent than orbital transitions, their typical coupling strengths have been estimated to be much smaller. Hence, they have been neglected for the purposes of quantum information technology.\nHowever, we predict that strong coupling is feasible between photons and a ferromagnetic nanomagnet, due to exchange interactions that cause very large numbers of spins to coherently lock together with a significant increase in oscillator strength while still maintaining very long coherence times. In order to examine this new exciting possibility, the interaction of a ferromagnetic nanomagnet with a single photonic mode of a cavity is analyzed in a fully quantum-mechanical treatment. Exceptionally large quantum-coherent magnet-photon coupling with coupling terms in excess of several THz are predicted to be achievable in a spherical cavity of ∼ 1 mm radius with a nanomagnet of ∼ 100 nm radius and ferromagnet resonance frequency of ∼ 200 GHz. This should substantially exceed the coupling observed in solids between orbital transitions and light. Eigenstates of the nanomagnet-photon system correspond to entangled states of spin orientation and photon number over 105 values of each quantum number. Initial coherent state of definite spin and photon number evolve dynamically to produce large coherent oscillations in the microwave power with exceptionally long dephasing times of few seconds. In addition to dephasing, several decoherence mechanisms including elementary excitation of magnons and crystalline magnetic anisotropy are investigated and shown to not substantially affect coherence upto room temperature. For small nanomagnets the crystalline magnetic anisotropy of the magnet strongly localize the eigenstates in photon and spin number, quenching the potential for coherent states and for a sufficiently large nanomagnet the macrospin approximation breaks down and different domains of the nanomagnet may couple separately to the photonic mode. Thus the optimal nanomagnet size is predicted to be just below the threshold for failure of the macrospin approximation. Moreover, it is shown that initially unentangled coherent states of light (cavity field) and spin (nanomagnet spin orientation) can be phase-locked to evolve into a coherent entangled states of the system under the influence of strong coupling.
Interaction of the vacuum field of an optical mode with an electronic two-level system can drive non-perturbative light-matter dynamics, resulting in an exotic quantum ground state containing a sizeable population of virtual excitations. In the deep-strong coupling (DSC) regime, where the Rabi frequency,ΩR\Omega_{\mathrm{R}}ΩR​, exceeds the eigen-frequencies of the coupled systems, this extreme ground state can result in spectacular effects of cavity-QED, such as the expected release of the virtual photon ground state population as vacuum radiation by non-adiabatic modulation of the coupling mechanism [1], [2]. However, for resonant coupling of two single modes [3], the finite oscillator strength of resonant electronic excitation sets a natural limit to the achievable coupling strength, hindering further exploration of this exciting field.
Understanding physical properties of quantum emitters strongly interacting with quantized electromagnetic modes is one of the primary goals in the emergent field of waveguide quantum electrodynamics (QED). When the light-matter coupling strength is comparable to or even exceeds energies of elementary excitations, conventional approaches based on perturbative treatment of light-matter interactions, two-level description of matter excitations, and photon-number truncation are no longer sufficient. Here we study in and out of equilibrium properties of waveguide QED in such nonperturbative regimes on the basis of a comprehensive and rigorous theoretical approach using an asymptotic decoupling unitary transformation. We uncover several surprising features ranging from symmetry-protected many-body bound states in the continuum to strong renormalization of the effective mass and potential; the latter may explain recent experiments demonstrating cavity-induced changes in chemical reactivity as well as enhancements of ferromagnetism or superconductivity. To illustrate our general results with concrete examples, we use our formalism to study a model of coupled cavity arrays, which is relevant to experiments in superconducting qubits interacting with microwave resonators or atoms coupled to photonic crystals. We examine the relation between our results and delocalization-localization transition in the spin-boson model; notably, we point out that a reentrant transition can occur in the regimes where the coupling strength becomes the dominant energy scale. We also discuss applications of our results to other problems in different fields, including quantum optics, condensed matter physics, and quantum chemistry.
The prototypical system constituted by a two-level atom interacting with a quantized single-mode electromagnetic field is described by the quantum Rabi model (QRM). The QRM is potentially valid at any light-matter interaction regime, ranging from the weak (where the decay rates exceeds the coupling rate) to the deep strong coupling (where the interaction rate exceeds the bare transition frequencies of the subsystems). However, when reaching the ultrastrong coupling regime, several theoretical issues may prevent the correct description of the observable dynamics of such a system: (i) the standard quantum optics master equation fails to correctly describe the interaction of this system with the reservoirs; (ii) the correct output photon rate is no longer proportional to the intracavity photon number; and (iii) they appear to violate gauge invariance. Here, we study the photon flux emission rate of this system under the incoherent excitation of the two-level atom for any light-matter interaction strength and consider different effective temperatures. The dependence of the emission spectra on the coupling strength is the result of the interplay between energy levels, matrix elements of the observables, and the density of states of the reservoirs. Within this approach, we also study the occurrence of light-matter decoupling in the deep strong-coupling regime and show how all of the obtained results are gauge invariant.