The goal of our research is to advance fundamental understanding of light-matter interactions at subwavelength scale. We utilize both classical and quantum theories to scrutinize general physical aspects of optical properties of various materials ranging from dispersive dielectrics to nonlinear crystals. Such systems exhibit interesting phenomena, some of which we use to investigate how individual atoms and molecules behave in the vicinity of these materials. For example, silver diffraction gratings may support strong electromagnetic field gradients as shown in the figure on the left. These gradients may be used to trap quantum objects. Our group has various collaborators around the world including such well-established schools as Northwestern University, University of Illinois at Chicago, Tel Aviv University, Weizman Institute of Science, University of Paris South (Orsay), and others.

research highlights

Non-Hermitian wave packet approximation of Bloch optical equations

see our recent JCP paper

In collaboration with Prof. Eric Charron (University of Paris South XI, Orsay, France) we have recently launched a new project: electrodynamics of ensembles of interacting molecules strongly coupled to plasmonic materials. In addition to active electronic transitions we are accounting for ro-vibrational structure and exploring its influence on collective modes of various nano-systems. In order to speed up already heavy calculations based on self-consistent Maxwell-Schrodinger equations we proposed a new approximation. We introduce a new non-Hermitian approximation of Bloch equations. This approximation provides a complete description of the excitation, relaxation and decoherence dynamics of single as well as ensembles of coupled quantum emitters (atoms or molecules) in weak laser fields, taking into account collective effects and dephasing. This is demonstrated by computing the numerical wave packet solution of a time-dependent non-Hermitian Maxwell-Schrodinger equation describing the interaction of electromagnetic radiation with a quantum (atomic or molecular) nano-structure and by comparing the calculated transmission, reflection, and absorption spectra with those obtained from the numerical solution of the Maxwell-Liouville-von Neumann equation. We provide the key ingredients for easy-to-use implementation of the proposed scheme using time-dependent decay rates and identify the limits and error scaling of this approximation.

Absorption spectra A(E) calculated for a molecular layer (comprised of Li2 molecules) of thickness ∆z = 400 nm as a function of the incident photon energy E. The molecular density is n = 2.5 × 1025 m−3. in the left column (panels (a) and (b)) and n = 2.5 × 1027 m−3. in the right column (panels (c) and (d)). The solutions of Maxwell-Liouville-von Neumann equations are shown as blue solid lines in the first raw (panels (a) and (c)) while the red solid lines (inverted spectra, panels (b) and (d)) are from the solutions of our approximate non-Hermitian Schrodinger model.

Coherent control of energy transfer in hybrid systems driven by strong laser pulses

In collaboration with Tamar Seideman, Robert Gordon, Yehiam Prior, Adi Salomon we initiated a new research project: transient spectroscopy of hybrid systems. Following our recent paper in Phys. Rev. Lett. we scrutinize nonlinear dynamics of ensembles of quantum emitters strongly coupled to plasmons.

The ability to monitor optical properties (such as absorption, reflection, transmission) modified by a strong pump is a major advantage of the transient spectroscopy technique. It allows to track internal changes of an optically active system driven by a pump as functions of time. Even though experimental procedures are technically challenging many experimental groups are capable of performing such measurements. Notwithstanding the progress in theory, self-consistent simulations have not yet been applied to model pump-probe experiments in hybrid systems.

We consider a thin layer of molecules (of the same thickness of 10 nm as in previous section) deposited onto a periodic array of slits with the geometry of the problem and molecular energy diagram as in our recent PRL paper. Each emitter has a transition frequency of 1.61 eV to match corresponding plasmon resonance for the slit array. Our main goal is to simulate the response of this system to an external femtosecond laser pulse (we use 180 fs long pulses). Both linear and nonlinear responses of the hybrid system is calculated using self-consistent model based on Maxwell-Liouville-von Neumann equations.

Probing the unperturbed system results in a transmission spectrum shown in figure below. We can see all three resonances – lower polariton (LP) at 1.53 eV, upper polariton (UP) at 1.69 eV, and collective mode (CM) at 1.62 eV. We are interested in observing Rabi oscillations between these states. The question is whether CM state plays any role in such a dynamics. And if it does how it modifies the energy transfer between LP and UP states.

Normalized transmission as a function of the incident energy for 410 nm slit array with a 10 nm layer of molecules on top.

Figure below shows transmission as a function of the incident energy and delay for the peak amplitude of the pump of 4.3x106 V/cm. Oscillations between LP, CM, and UP states are clearly present. Moreover energy is oscillating to and from CM, while LP and UP states oscillate in phase, i.e. the energy from them is transferred to CM state and back. The period of oscillations, Tmodel, is 25 fs.

Upper panel transmission as a function of the incident energy and delay for the 180 fs pump at 4.3x106 V/cm. Lower panel shows 1D cuts of the transmission as functions of the delay for three states – LP (1.53 eV), CM (1.62 eV), UP (1.69 eV).

Highly inhomogeneous electric fields increase dephasing, which in turn could be easily obtained from transient spectra shown in figure above. Another simulations (not shown) with a different period show that one can control the energy transfer by varying the k-vector of plasmons (i.e. the coupling between plasmons and molecules) – one can suppress energy transfer to either LP or UP states keeping intact energy transfer to and from CM state.