Semi-empirical quantum optics for mid-infrared molecular nanophotonics

Abstract

Nanoscale infrared (IR) resonators with sub-diffraction limited mode volumes and open geome- tries have emerged as new platforms for implementing cavity QED at room temperature. The use of infrared (IR) nano-antennas and tip nanoprobes to study strong light-matter coupling of molecular vibrations with the vacuum field can be exploited for IR quantum control with nanometer and femtosecond resolution. To accelerate the development of molecule-based quantum nano-photonic devices in the mid-IR, we propose a generally applicable semi-empirical methodology based on quantum optics to describe light-matter interaction in systems driven by femtosecond laser pulses. The theory is shown to reproduce recent experiments on the acceleration of the vibrational relaxation rate in infrared nanostructures, and also provide phys- ical insights for the implementation of coherent phase rotations of the near-field using broadband nanotips. We then apply the quantum framework to develop general tip-design rules for the exper- imental manipulation of vibrational strong coupling and Fano interference effects in open infrared resonators. We finally propose the possibility of transferring the natural anharmonicity of molecular vibrational levels to the resonator near-field in the weak coupling regime to implement intensity-dependent phase shifts of the coupled system response with strong pulses, and develop a vibrational chirping model to understand the effect. The semi-empirical quantum theory is equivalent to first- principles techniques based on Maxwell's equations, but its lower computational cost suggests its use a rapid design tool for the development of strongly-coupled infrared nanophotonic hardware for applications ranging from quantum control of materials to quantum information processing.

Control, Modulation, and Analytical Descriptions of Vibrational Strong Coupling

“…Detailed examination of the dynamics of this coupled system revealed accelerated dephasing . Although initially attributing an apparently reduced population decay time to very high cavity Purcell factors > 10 6 , a semiempirical open quantum system model explained this effect in terms of a more modest vibrational Purcell effect (on the order of a few) due to the fast-decaying nanoantenna resonator mode. This more comprehensive model exposed possible anharmonic blockade effects that could lead to nonlinear population of vibrational excitations and optical transformation of the electromagnetic field potentially relevant to quantum optical processing.…”

Coherent anharmonicity transfer from matter to light in the THz regime

“…For the open cavity field, the main source of decoherence is non radioactive decay in the metal [73], as well as radioactive losses. In this work, the light-matter system is considered to be in the weak coupling regime, broadly defined by the absence of vacuum Rabi splitting in linear transmission [36], which results from a small cooperativity parameter Ng 2 /κγ < 1. The time-dependent Hamiltonian Ĥd (t) that describes the driving pulse is given by…”

“…This is red shifted from the fundamental resonance by an amount proportional to the bright mode occupation. The nonlinearity is proportional to the anharmonicity parameter U and is small for large N [36]. The transient red shift occurs while the system is driven by the laser pulse, which populates B0 (t), and is thus proportional to the photon flux parameter F 0 .…”

“…The enhancement of the spontaneous emission rate of material dipoles in a weakly coupled cavity via the Purcell effect [27][28][29] has been used over different frequency regimes for reservoir engineering [30,31], dipole cooling [32,33] and quantum state preparation [34]. In infrared cavities, the Purcell effect can be an effective tool for studying the relaxation dynamics of THz transitions in materials [35][36][37], given the negligible radioactive decay rates at these frequencies in comparison with non-radioactive relaxation processes [38,39]. The direct linear measurement of confined infrared field dynamics in a weakly coupled dipole-cavity system [40] can thus provide information about infrared transitions that otherwise would only be accessible using ultrasfast nonlinear spectroscopy [41,42].…”

“…To emphasize the feasibility of implementing the proposed phase nonlinearity using current technology, the relevant frequency scales of the problem are specified according to recent cavity QED experiments with intersubband transitions of multi quantum wells (MQWs) embedded in infrared nanoresonators [16]. The proposed scheme should be simpler with MQW than ensembles of molecular vibrations [36], because the number of dipoles is much smaller and the spectral anharmonicity much higher. By driving the resonator with a moderately strong femtosecond laser pulse, the matter-induced phase nonlinearity can be retrieved from the free-induction decay (FID) of the resonator near field E nf (t) using linear heterodyne spectroscopy techniques with femtosecond time resolution [35,37,[63][64][65][66][67].…”