Collective Optomechanical Effects in Cavity Quantum Electrodynamics

Abstract

We investigate a cavity quantum electrodynamic effect, where the alignment of two-dimensional freely rotating optical dipoles is driven by their collective coupling to the cavity field. By exploiting the formal equivalence of a set of rotating dipoles with a polymer we calculate the partition function of the coupled light-matter system and demonstrate it exhibits a second order phase transition between a bunched state of isotropic orientations and a stretched one with all the dipoles aligned. Such a transition manifests itself as an intensity-dependent shift of the polariton mode resonance. Our work, lying at the crossroad between cavity quantum electrodynamics and quantum optomechanics, is a step forward in the on-going quest to understand how strong coupling can be exploited to influence matter internal degrees of freedom.When the energy exchange between an optically active dipolar transition and a resonant electromagnetic cavity mode becomes faster than any relaxation process, we enter the so-called strong coupling regime. In such a regime a description of the system in terms of light and matter exchanging energy through emission and absorption processes fails, and it becomes necessary to consider its coupled eigenmodes. When many independent dipoles are coupled with the same cavity photonic mode, the collective light-matter coupling scales with the square root of the number of dipoles [1], making it possible to modify the coupling by engineering the dipole density. The normal modes of those systems are called polaritons, quasi-bosonic [2] half-light and half-matter quasiparticles. They have been observed to date in a number of different cavity quantum electrodynamics implementations, both in atomic physics, using cold atoms [3][4][5][6][7], and in many solid-state system, from microcavity-embedded semiconductor quantum wells to magnetic spheres in microwave cavities [8][9][10][11][12][13][14][15].

Orientational alignment in cavity quantum electrodynamics

“…(1) because the two-level systems are saturable. However, such effects were shown in [44] to not significantly change the behavior. (We also consider this further below.)…”

“…The solution of this equation increases from x 0 = 0 at a = 0 to reach x 0 = 1 when a = 8. By definition, |x 0 | < 1, and so this Gaussian polymer approximation predicts that at a = 8, a second order transition occurs to a fully ordered state [44].…”

“…A number of different theoretical frameworks have been used for tackling these problems. These include using symmetries to reduce the problem size, and mean-field theories [6,[42][43][44][45]. From the context of condensed matter physics, mean-field theory is a natural approach.…”

Cavity Casimir-Polder Forces and Their Effects in Ground-State Chemical Reactivity

“…The details of this effect depend on the precise setup, such as the cavity material and shape, molecular and solvent properties, etc., and would require a more complete treatment taking thermodynamical effects and free energy into account [111,112], which is beyond the scope of the current work. However, we mention that it has recently been shown that strong coupling and the associated formation of polaritons itself could lead to alignment due to the associated decrease of the lower polariton energy, provided that a significant fraction of molecules are excited to lower polariton states [29,113]. Although thermal excitation can be efficient for vibrational strong coupling due to the relatively low energies of vibro-polaritons, on the order of a few times the thermal energy k B T , it should be noted that the arguments in [29,113] do not directly translate to thermal-equilibrium situations.…”

Strong coupling of ionizing transitions

“…Many works demonstrated how the hybridization with matter strongly alters not only the spectrum, but also the field profile [2][3][4], and the quantum [5][6][7][8] and nonlinear [9,10] properties of the photonic resonator. More recently interest has also broadened to investigate how strong coupling can be used to modify properties of the underlying matter degrees of freedom [11][12][13][14][15][16][17][18], including changes in electrical [19][20][21][22][23] and photochemical [24][25][26][27] properties.…”