Quantum vacuum properties of the intersubband cavity polariton field

Abstract

We present a quantum description of a planar microcavity photon mode strongly coupled to a semiconductor intersubband transition in presence of a two-dimensional electron gas. We show that, in this kind of system, the vacuum Rabi frequency ΩR can be a significant fraction of the intersubband transition frequency ω12. This regime of ultra-strong light-matter coupling is enhanced for long wavelength transitions, because for a given doping density, effective mass and number of quantum wells, the ratio ΩR/ω12 increases as the square root of the intersubband emission wavelength. We characterize the quantum properties of the ground state (a two-mode squeezed vacuum), which can be tuned in-situ by changing the value of ΩR, e.g., through an electrostatic gate. We finally point out how the tunability of the polariton quantum vacuum can be exploited to generate correlated photon pairs out of the vacuum via quantum electrodynamics phenomena reminiscent of the dynamical Casimir effect.In the last decade, the study of intersubband electronic transitions 1 in semiconductor quantum wells has enjoyed a considerable success, leading to remarkable opto-electronic devices such as the quantum cascade lasers 2,3,4 . In contrast to the more conventional interband transitions between conduction and valence bands, the frequency of intersubband transitions is not determined by the energy gap of the semiconductor material system used, but rather can be chosen via the thickness of the quantum wells in the active region, providing tunable sources emitting in the mid and far infrared.One of the most fascinating aspects of light-matter interaction is the so-called strong light-matter coupling regime, which is achieved when a cavity mode is resonant with an electronic transition of frequency ω 12 , and the so-called vacuum Rabi frequency Ω R exceeds the cavity mode and electronic transition linewidths. The strong coupling regime has been first observed in the late '80s using atoms in metallic cavities 5,6 , and a few years later in solid-state systems using excitonic transitions in quantum wells embedded in semiconductor microcavities 7 . In this regime, the normal modes of the system consist of linear superpositions of electronic and photonic excitations, which, in the case of semiconductor materials, are the so-called polaritons. In both these systems, the vacuum Rabi frequency Ω R does not exceed a very small fraction of the transition frequency ω 12 .Recently, Dini et al. 8 have reported the first demonstration of strong coupling regime between a cavity photon mode and a mid-infrared intersubband transition, in agreement with earlier semiclassical theoretical predictions by Liu 9 . The dielectric Fabry-Perot structure realized by Dini et al. 8 consists of a modulation doped multiple quantum well structure embedded in a microcavity, whose mirrors work thanks to the principle of total internal reflection. The strong coupling regime has been also observed in quantum well infra-red detectors 10 . As we will show in detail, an important advant...

Subcycle measurement of intensity correlations in the terahertz frequency range

“…Placed at mid-way between the optics and the microwave, the Terahertz frequency region (100 GHz-10 THz) is potentially very interesting beyond its advanced applications in spectroscopy [6,7] or matter control [8] for the study of linear or nonlinear quantum phenomena at the ultra-strong coupling limit of light-matter interaction [9]. This limit is specifically accessible in this frequency range because of the successful implementation of metallic cavities with strongly subwavelength effective volumes [10] which can be combined with quantum heterostructures in semconductors to form hybrid systems [11,12].…”

Collective non-perturbative coupling of 2D electrons with high-quality-factor terahertz cavity photons

“…However, the large values of ω 0 and relatively small dipole moments for interband transitions make it impractical to achieve large values of g/ω 0 using exciton-polaritons. Intraband transitions, such as intersubband transitions (ISBTs) [1] and cyclotron resonance (CR) [22], are much better candidates for accomplishing ultrastrong coupling because of their small ω 0 , typically in the midinfared and terahertz (THz) range, and their enormous dipole moments (10s of e-Å). Experimentally, ultrastrong coupling has indeed been achieved in GaAs QWs using ISBTs [10,11] and CR [12,13].…”

“…For example, collective √ N -fold enhancement of light-matter coupling in an N -body system [19], combined with colossal dipole moments available in solids, compared to traditional atomic systems, is promising for entering uncharted regimes of ultrastrong light-matter coupling. Nonintuitive quantum phenomena can occur in such regimes, including a "squeezed" vacuum state [1], the Dicke superradiant phase transition [2,3], the breakdown of the Purcell effect [4], and quantum vacuum radiation [5] induced by the dynamic Casimir effect [6,7].…”

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Nonperturbative coupling of light with condensed matter in an optical cavity is expected to reveal a host of coherent many-body phenomena and states [1][2][3][4][5][6][7]. In addition, strong coherent light-matter interaction in a solid-state environment is of great interest to emerging quantum-based technologies [8,9].

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Heisenberg uncertainty principle as a probe of entanglement entropy: Application to superradiant quantum phase transitions

“…It is also important to compare the criticality given by the mean-field with some finite size results. First, in the limit λ/ω → ∞ (the so-called ultrastrong coupling limit [28][29][30]), a N th order perturbative theory allows to prove that the two first eigenstates |Ψ G and |Ψ E , have their energies separated by an exponentially small splitting, and are linear superpositions of the states |α F |N/2 x and |−α F |−N/2 x . Here, |±α F are coherent states for the photonic part: a| ± α F = ±α F | ± α F with ±α F = ± √ N λ/ω [31,32].…”