Standing-wave Light Field Research Articles

Resonant Stimulated Photorefractive Scattering.

We present the first observations, and a complete theoretical explanation, of stimulated photorefractive scattering in a high- Q crystalline cavity. The standing-wave light field in the cavity induces an ultranarrow and long-lived Bragg grating through the photorefractive effect. The spatial phase of the grating is automatically matched to that of the standing wave. The scattering from the grating strengthens the standing wave, which then further reinforces the grating itself. Eventually, the mode is seen to split into a doublet, thereby disrupting the usual strict periodicity of the mode spectrum.

Experimental Observation of Momentum-Space Chiral Edge Currents in Room-Temperature Atoms.

Chiral edge currents play an important role in characterizing topological matter. In atoms, they have been observed at such a low temperature that the atomic motion can be measured. Here we report the first experimental observation of chiral edge currents in atoms at room temperature. Staggered magnetic fluxes are induced by the spatial phase difference between two standing-wave light fields, which couple atoms to form a momentum-space zigzag superradiance lattice. The chiral edge currents are measured by comparing the directional superradiant emissions of two timed Dicke states in the lattice. Our results pave the way for simulating topological physics in hot atoms.

Hybrid Photon-Plasmon Coupling and Ultrafast Control of Nanoantennas on a Silicon Photonic Chip.

Hybrid integration of nanoplasmonic devices with silicon photonic circuits holds promise for a range of applications in on-chip sensing, field-enhanced and nonlinear spectroscopy, and integrated nanophotonic switches. Here, we demonstrate a new regime of photon-plasmon coupling by combining a silicon photonic resonator with plasmonic nanoantennas. Using principles from coherent perfect absorption, we make use of standing-wave light fields to maximize the photon-plasmon interaction strength. Precise placement of the broadband antennas with respect to the narrowband photonic racetrack modes results in controlled hybridization of only a subset of these modes. By combining antennas into groups of radiating dipoles with opposite phase, far-field scattering is effectively suppressed. We achieve ultrafast tuning of photon-plasmon hybridization including reconfigurable routing of the standing-wave input between two output ports. Hybrid photonic-plasmonic resonators provide conceptually new approaches for on-chip integrated nanophotonic devices.

Ionization of Rydberg atoms by standing-wave light fields

When electromagnetic radiation induces atomic transitions, the size of the atom is usually much smaller than the wavelength of the radiation, allowing the spatial variation of the radiation field's phase to be neglected in the description of transition rates. Somewhat unexpectedly, this approximation, known as the electric dipole approximation, is still valid for the ionization of micrometre-sized atoms in highly excited Rydberg states by laser light with a wavelength of about the same size. Here we employ a standing-wave laser field as a spatially resolving probe within the volume of a Rydberg atom to show that the photoionization process only occurs near the nucleus, within a volume that is small with respect to both the atom and the laser wavelength. This evidence resolves the apparent inconsistency of the electric dipole approximation's validity for photoionization of Rydberg atoms, and it verifies the theory of light-matter interaction in a limiting case.

Precision measurement of resonate frequency and the effective cavity length of the high finesse optical micro-cavity

Ultra-high finesse micro-resonator plays an important role in realizing the interaction between atoms and cavity field in the study of cavity quantum electrodynamics (QED) system, weak optical nonlinear effects and micro-optic devices. By measuring basic parameters of the microcavity, the atom-cavity coupling coefficient and the cavity decay rate can be determined precisely. It is also useful for exploring the dynamic characteristics of the system. However, it has difficulty in determining resonate frequency and effective cavity length due to the structure of the ultra-high finesse optical microcavity itself and the characteristics of multilayer coating. In this paper, we demonstrate the precision measurement of effective cavity length under different resonant frequencies which our cavity mirror is coated with 37 layers of dielectric film. The theoretical expectation when using the revised model of the multilayer coating agrees well with that of the experiment; and the measurement error for longitudinal mode interval is below 0.004 nm which is two orders of magnitude better than that obtained in previous unrevised model. The tiny depths into mirror coatings that the standing-wave light field inside the cavity penetrates are given for different mode numbers. This method may be applied to other micro resonator in the precision measurement.

Structure formation in atom lithography using geometric collimation

Atom lithography uses standing wave light fields as arrays of lenses to focus neutral atom beams into line patterns on a substrate. Laser cooled atom beams are commonly used, but an atom beam source with a small opening placed at a large distance from a substrate creates atom beams which are locally geometrically collimated on the substrate. These beams have local offset angles with respect to the substrate. We show that this affects the height, width, shape, and position of the created structures. We find that simulated effects are partially obscured in experiments by substrate-dependent diffusion of atoms, while scattering and interference just above the substrate limit the quality of the standing wave lens. We find that in atom lithography without laser cooling the atom beam source geometry is imaged onto the substrate by the standing wave lens. We therefore propose using structured atom beam sources to image more complex patterns on subwavelength scales in a massively parallel way.

Subwavelength optical lattices induced by position-dependent dark states

A method for the generation of subwavelength optical lattices based on multilevel dark states is proposed. The dark state is formed by a suitable combination of standing wave light fields, leading to position-dependent populations of the ground states. An additional field coupling dispersively to one of the ground states translates this position dependence into a subwavelength optical potential. We provide two semiclassical approaches to understand the involved physics, and demonstrate that they lead to identical results in a certain meaningful limit. Then we apply a Monte Carlo simulation technique to study the full quantum dynamics of the subwavelength trapping. Finally, we discuss the relevant time scales for the trapping, optimum conditions, and possible implementations.

Stationary light pulses in cold thermal atomic clouds

Fourier-expanded Maxwell-Liouville equations are employed to study the light pulse dynamics in atomic samples coherently driven by a standing-wave light field. Solutions are obtained by a suitable truncation of the Maxwell-Liouville equations that contain the number of spin and optical Fourier coherence components appropriate to the sample temperature. This approach is examined here for cold but thermal atoms where the Doppler broadening is still not negligible and familiar secular approximations no longer hold. In this temperature regime higher-order momentum Fourier coherence components are shown to be important for achieving excellent agreement with a recent experiment done in cold $^{87}\mathrm{Rb}$ clouds at several hundred microkelvins.

Proliferation of atomic wave packets at the nodes of a standing light wave

A quantum analysis is presented of the motion and internal state of a two-level atom in a strong standing-wave light field. Coherent evolution of the atomic wave-packet, atomic dipole moment, and population inversion strongly depends on the ratio between the detuning from atom-field resonance and a characteristic atomic frequency. In the basis of dressed states, atomic motion is represented as wave-packet motion in two effective optical potentials. At exact resonance, coherent population trapping is observed when an atom with zero momentum is centered at a standing-wave node. When the detuning is comparable to the characteristic atomic frequency, the atom crossing a node may or may not undergo a transition between the potentials with probabilities that are similar in order of magnitude. In this detuning range, atomic wave packets proliferate at the nodes of the standing wave. This phenomenon is interpreted as a quantum manifestation of chaotic transport of classical atoms observed in earlier studies. For a certain detuning range, there exists an interval of initial momentum values such that the atom simultaneously oscillates in an optical potential well and moves as a ballistic particle. This behavior of a wave packet is a quantum analog of a classical random walk of an atom, when it enters and leaves optical potential wells in a seemingly irregular manner and freely moves both ways in a periodic standing light wave. In a far-detuned field, the transition probability between the potentials is low, and adiabatic wave-packet evolution corresponding to regular classical motion of an atom is observed.

Isotope separation via atom optics in the Bragg regime

We study the resonant interaction of a beam of mono-velocity two-level atoms with a standing-wave light field in the Bragg regime. The atomic beam consists of two different isotopes, and the density is sufficiently small so that at most one atom is inside the cavity at a time. The momentum transfer between the atoms and photons in the process significantly effects the center-of-mass motion of the atoms, thus separating the isotopes in different directions.

Atomic beam splitter from a mixture of atoms in the Bragg regime

We investigate the interaction of a standing-wave light field with the beam of two-level atoms moving in the Bragg regime. The atomic beam consists of two different isotopes and the density is sufficiently small so that at most one atom is inside the cavity at any time. The experimental setup is such that both the isotopes have the same momenta. The momentum transfer between the atoms and photons in the process essentially effects the center-of-mass motion of the atoms, thus separating the isotopes in different directions after specific interaction times.

Laser cooling of an indium atomic beam enabled by magnetic fields

We demonstrate magnetic field enabled optical forces on a neutral indium atomic beam in a light field consisting of five frequencies. The role of dark magnetic ground state sublevels is studied and enables us to cool the atomic beam transversely to near the Doppler limit with laser frequencies tuned above the atomic resonance. The effect of laser cooling can be explained with transient effects in the light potential created by the standing wave light field where the atoms are optically pumped into the dark states and recycled by Larmor precession.

Simulation of laser-induced nanopattern formation

Over the last decade it has been shown theoretically and experimentally that a near-resonant standing wave light field can be used during deposition to deflect collimated neutral atoms, thereby constraining them to form periodic structures. Another effect studied in recent experiments is that a laser interference pattern in contact with a substrate can also result in patterns mimicking the interference fringes. This patterning has tentatively been attributed to thermal gradients resulting from non-uniform heating induced by the interference patterns. We developed a model and a computer program to investigate the possibility of making these two laser effects interact constructively to refine the resolution. The simulations proceed in two stages: first, atom trajectories in a laser field are simulated using classical-mechanical equations of motion in an effective potential to obtain the deposition profile; then, the obtained profile is used as an input in a kinetic Monte Carlo (KMC) simulation of atom diffusion on a substrate with spatially varying temperature. Our results show substantial improvement in quality of the patterns compared to that achieved by using either effect alone. We examine many growth conditions in addition to the different laser parameter settings for optimal constructive interference of the two effects. The computer code used in the simulations is designed to run efficiently on both simple PC platforms and supercomputers; its design, data structures used and other features are described in detail.

Theoretical calculation of saturated absorption spectra for multi-level atoms

We have developed a model for calculating saturated absorption spectra for dipole transitions in multi-level atoms. Using a semiclassical density matrix formalism, we derive a set of coupled differential equations for the internal state of the atom in a standing wave light field. The equations are solved using standard integration techniques. The absorption at each laser detuning is found from an average of the absorption for a number of velocities along the laser field, thermally weighted. The method is relatively efficient computationally yet quantitatively predicts important details of saturated absorption spectra including saturation, crossover resonances, merging of absorption lines at high intensity and optical pumping between hyperfine levels. We have measured saturated absorption and fluorescence spectra of 85Rb, and compare to our computational results for a 36-level model.

Quantum interference induced sub-wavelength atomic localization*

We investigate how observation of upper state atomic populations localize atomic position distributions for three-level atoms within a classical standing wave light field. We consider a three-level atom, with the standing wave near-resonantly coupling one transition and a probe laser field near-resonantly coupling the second transition. Two different cases of localization are identified and we explore the dependence of localization on the parameters of the field–atom interaction.

Time domain de Broglie wave interferometry along a magnetic guide

Time domain deBroglie wave interferometry [Cahn et al, Phys. Rev. Lett. 79, 784] is applied to Rb87 atoms in a magnetic guide. A standing wave light field is carefully aligned along the guiding direction of the magnetic trapping potential from a soft-ferromagnetic 4-foil structure. A sequence of two standing wave pulses is applied to the magnetically trapped atoms. The backscattered light at the atomic density grating revival time is collected and detected via a heterodyning technique. In addition to the observed recoil oscillations that fit the interferometer theory for atoms in free space, we observe a decay of the interferometer contrast on a millisecond time scale with unexpected millisecond-scale oscillations. We find that the oscillating decay is explained by a residual variation of the linear trapping potential along the standing wave direction.

Atom Michelson Interferometer on a Chip Using a Bose-Einstein Condensate

An atom Michelson interferometer is implemented on an "atom chip." The chip uses lithographically patterned conductors and external magnetic fields to produce and guide a Bose-Einstein condensate. Splitting, reflecting, and recombining of condensate atoms are achieved by a standing-wave light field having a wave vector aligned along the atom waveguide. A differential phase shift between the two arms of the interferometer is introduced by either a magnetic-field gradient or with an initial condensate velocity. Interference contrast is still observable at 20% with an atom propagation time of 10 ms.

Nanolithography with metastable helium atoms in a high-power standing-wave light field

We have created periodic nanoscale structures in a gold substrate with a lithography process using metastable triplet helium atoms that damage a hydrophobic resist layer on top of the substrate. A beam of metastable helium atoms is transversely collimated and guided through an intense standing-wave light field. Compared to commonly used low-power optical masks, a high-power light field (saturation parameter of 107) increases the confinement of the atoms in the standing wave considerably, and makes the alignment of the experimental setup less critical. Due to the high internal energy of the metastable helium atoms (20 eV), a dose of only one atom per resist molecule is required. With an exposure time of only eight minutes, parallel lines with a separation of 542 nm and a width of 100 nm (one-eleventh of the wavelength used for the optical mask) are created.

Numerical simulations on the motion of atoms travelling through a standing-wave light field

The motion of metastable helium atoms travelling through a standing light wave is investigated with a semi-classical numerical model. The results of a calculation including the velocity dependence of the dipole force are compared with those of the commonly used approach, which assumes a conservative dipole force. The comparison is made for two atom guiding regimes that can be used for the production of nanostructure arrays; a low power regime, where the atoms are focused in a standing wave by the dipole force, and a higher power regime, in which the atoms channel along the potential minima of the light field. In the low power regime the differences between the two models are negligible and both models show that, for lithography purposes, pattern widths of 150 nm can be achieved. In the high power channelling regime the conservative force model, predicting 100 nm features, is shown to break down. The model that incorporates velocity dependence, resulting in a structure size of 40 nm, remains valid, as demonstrated by a comparison with quantum Monte-Carlo wavefunction calculations.

Bistability and macroscopic quantum coherence in a Bose-Einstein condensate of7Li

We consider a Bose-Einstein condensate (BEC) of $^7Li$ in a situation where the density undergoes a symmetry breaking in real space. This occurs for a suitable number of condensed atoms in a double well potential, obtained by adding a standing wave light field to the trap potential. Evidence of bistability results from the solution of the Gross-Pitaevskii equation. By second quantization, we show that the classical bistable situation is in fact a Schr\"odinger cat (SC) and evaluate the tunneling rate between the two SC states. The oscillation between the two states is called MQC (macroscopic quantum coherence); we study the effects of losses on MQC.