Standing-wave Cavity Mode Research Articles

An angle-tuned polarization-independent multi-narrowband perfect absorber

We propose and numerically investigate an angle-tuned polarization-independent multi-narrowband perfect absorber, which comprises a simple gold nanocube array on SiO2/oxidized aluminum mirror layers. The oxidized aluminum mirror is able to support the surface plasmon polariton mode on the SiO2/Al2O3 interface. The multi-narrowband absorption contributes to the simultaneously excited quasi-metal–insulator–metal guided modes and standing wave cavity mode in the thick insulator layer by the incident light normal to the structure in the wavelength range 1400–2400 nm. Moreover, the absorption can be actively modulated by adjusting the incidence angle, and it is polarization independent. The perfect absorber is also suitable for sensing, with the figure of merit reaching 102 RIU−1 within the refractive index range from 1.3 to 1.36.

Many-body phases of a planar Bose-Einstein condensate with cavity-induced spin-orbit coupling

We explore the many-body phases of a two-dimensional Bose-Einstein condensate with cavity-mediated dynamic spin-orbit coupling. By the help of two transverse non-interfering, counterpropagating pump lasers and a single standing-wave cavity mode, two degenerate Zeeman sub-levels of the quantum gas are Raman coupled in a double-$\Lambda$-configuration. Beyond a critical pump strength the cavity mode is populated via coherent superradiant Raman scattering from the two pump lasers, leading to the appearance of a dynamical spin-orbit coupling for the atoms. We identify three quantum phases with distinct atomic and photonic properties: the normal ``homogeneous'' phase, the superradiant ``spin-helix'' phase, and the superradiant ``supersolid spin-density-wave'' phase. The latter exhibits an emergent periodic atomic density distribution with an orthorhombic centered rectangular-lattice structure due to the interplay between the coherent photon scattering into the resonator and the collision-induced momentum coupling. The transverse lattice spacing of the emergent crystal is set by the dynamic spin-orbit coupling.

Masked states of an atom coupled to a standing-wave cavity mode

The form of the eigenstates of an atom coupled to a cavity mode displaying a three dimensional periodic profile are obtained. It is shown that the quantized motion leads to degenerate states where the atomic degrees of freedom are masked, that is, upon detection of one component of this composite system the others remain in an entangled state. When the system is extended to include drive and dissipation it is found to undergo a dissipative quantum phase transition at a critical drive amplitude. Unlike other phase transitions reported in the literature, the degeneracy prepares the system in a superposition of incompatible states upon detection of the electromagnetic field. Probing the field hints at an order above the transition point that, due to state masking, allows for atomic coherence to survive at long times.

Hofstadter butterfly in a cavity-induced dynamic synthetic magnetic field

Energy bands of electrons in a square lattice potential threaded by a uniform magnetic field exhibit a fractal structure known as the Hofstadter butterfly. Here we study a Fermi gas in a 2D optical lattice within a linear cavity with a tilt along the cavity axis. The hopping along the cavity axis is only induced by resonant Raman scattering of transverse pump light into a standing wave cavity mode. Choosing a suitable pump geometry allows to realize the Hofstadter-Harper model with a cavity-induced dynamical synthetic magnetic field, which appears at the onset of the superradiant phase transition. The dynamical nature of this cavity-induced synthetic magnetic field arises from the delicate interplay between collective superradiant scattering and the underlying fractal band structure. Using a sixth-order expansion of the free energy as function of the order parameter and by numerical simulations we show that at low magnetic fluxes the superradiant ordering phase transition is first order, while it becomes second order for higher flux. The dynamic nature of the magnetic field induces a non-trivial deformation of the Hofstadter butterfly in the superradiant phase. At strong pump far above the self-ordering threshold we recover the Hofstadter butterfly one would obtain in a static magnetic field.

Terahertz band gaps induced by metal grooves inside parallel-plate waveguides

We report experimental and finite-difference time-domain simulation studies on terahertz (THz) characteristics of band gaps by using metal grooves which are located inside the flare parallel-plate waveguide. The vertically localized standing-wave cavity mode (SWCM) between the upper waveguide surface and groove bottom, and the horizontally localized SWCM between two groove side walls (groove cavity) are observed. The E field intensity of the horizontally localized SWCM in grooves is very strongly enchanced which is three order higher than that of the input THz. The 4 band gaps except the Bragg band gap are caused by the π radian delay (out of phase) between the reflected THz field by grooves and the propagated THz field through the air gap. The measurement and simulation results agree well.

Spontaneously created entanglement between two atoms

Spontaneous emission as a potential tool for creation of entanglement between two atoms is investigated. We assume that the atoms are coupled to the same environment and study entanglement engineering between the atoms and its transfer between different states. The role of the atomic coherence induced by spontaneous emission will be explored which, in contrast to what is generally believed, can create entanglement between initially unentangled atoms. We quantify entanglement by the concurrence and find that it exhibits threshold properties that can lead to interesting noncontinuous phenomena of sudden birth and sudden death of entanglement. In addition, we consider the mechanism involved in creation of entanglement between distant atoms coupled to a single-mode cavity field. We include a possible variation of the coupling constants between the atoms and the cavity mode with location of the atoms in a standing-wave cavity mode. Effectively, we engineer two coupled atoms whose the dynamics are analogous to that of interacting and collectively damped two nonidentical atoms. We illustrate the interesting result that spatial variations of the coupling constants can lead to a stationary entanglement between the atoms. We explain this effect in terms of the trapping phenomenon of atomic population in a non-decaying entangled state.

Effects of coupled bichromatic atom-cavity interaction in the cavity-QED microlaser

In the observation of multiple thresholds in the cavity-quantum electrodynamics microlaser there was deviation from the result predicted by uniform atom-cavity coupling theory, notably a frequency-pushing behavior. We analyze in the semiclassical limit the tilted injection of atoms, originally used to achieve a spatially uniform atom-cavity coupling, and show that the deviation originates from the interference between the induced dipole moments associated with two traveling-wave components of a standing-wave cavity mode. The criteria for sufficiently reduced interference and thus uniform atom-cavity interactions are derived in analytic considerations and verified by numerical calculation. Our analysis is well supported by experimental data.

Collective cooling and self-organization of atoms in a cavity.

We theoretically investigate the correlated dynamics of N coherently driven atoms coupled to a standing-wave cavity mode. For red detuning between the driving field and the cavity as well as the atomic resonance frequencies, we predict a light force induced self-organization of the atoms into one of two possible regular patterns, which maximize the cooperative scattering of light into the cavity field. Kinetic energy is extracted from the atoms by superradiant light scattering to reach a final kinetic energy related to the cavity linewidth. The self-organization starts only above a threshold of the pump strength and atom number. We find a quadratic dependence of the cavity mode intensity on the atom number, which demonstrates the cooperative effect.

Darkness of two entangled fluorescing atoms inside a quantized standing wave cavity

We study the center-of-mass motion of two two-level atoms coupled to a single quantized standing-wave cavity mode. Using an effective one-dimensional model in the one-excitation case, we obtain a general expression of the dark states, the entangled two atom states which are almost immune against photon escape from the cavity. We analyze the effects of the atomic dipole–dipole interaction and of fluorescence emission from the single atoms on the time evolution of the atom–cavity system.

Normal Mode Line Shapes for Atoms in Standing-Wave Optical Resonators.

A high finesse standing-wave cavity mode resonantly interacting with a beam of two-level ${}^{138}\mathrm{Ba}$ atoms is weakly driven by a tunable laser. Transmitted and sidelight scattered line shapes are recorded. With mean intracavity atomic number, $〈\overline{N}〉\ensuremath{\approx}1$, we observe one-, two-, and three-peaked line shapes for strong coupling. In addition, two-peaked spectra observed in intermediate coupling demonstrate that line-shape splitting is not necessarily indicative of oscillatory atom-cavity energy exchange. Several atoms are required for $〈\overline{N}〉\ensuremath{\approx}1$, so this is not a true single-atom regime.

Spontaneous emission in a standing-wave cavity: Quantum-mechanical center-of-mass motion.

We solve the spontaneous-emission problem for an atom coupled to a standing-wave cavity mode. The interaction between the atom and the cavity mode is treated nonperturbatively with the quantized motion of the atom along the cavity axis included. Results are presented for the spontaneous-emission spectrum and the final momentum distribution of the atom. For equal atomic and cavity linewidths analytical results are obtained using a Bloch-state basis (eigenstates of the coupled atom and cavity mode); these are compared with results calculated in the Raman-Nath approximation. The case of unequal linewidths may be solved numerically using the eigenstates of the uncoupled atom and cavity mode as a basis, or analytically by making a secular approximation in the Bloch-state basis. The distribution of final atomic momentum shows that under strong-coupling conditions the atom is diffracted by its radiation reaction field. We compare the spontaneous emission spectra with spectra calculated by treating the motion of the atom classically. Generally there is good agreement when the classical results are averaged over the quantum-mechanical uncertainty in the initial position of the atom. The agreement is lost for sufficiently strong dipole coupling or sufficiently light atoms. Then, spectra that are symmetric in the classical treatment are asymmetric in the quantum treatment due to energy exchange between the internal degrees of freedom and center-of-mass degrees of freedom of the atom.

Spontaneous emission in a standing-wave cavity: Classical center-of-mass motion.

We present a nonperturbative result for the spectrum of spontaneous photons emitted by an atom coupled on resonance to a standing-wave cavity mode. Motion of the atom through the standing-wave mode function is included in a classical way. We discuss the form of the spectrum as a function of the velocity of the atom in the limit of strong dipole coupling. For slow atoms the normal-mode doublet (``vacuum'' Rabi spectrum) survives with small changes. The motion of a fast atom through the standing wave averages the coupling constant to zero, and the spectrum reverts to a single peak. At intermediate velocities the spectrum has a complicated multipeaked structure that can be understood in terms of interfering probability amplitudes for different quantum-mechanical emission paths or as a frequency-modulation spectrum for radiating coupled oscillators.