Subnatural Linewidths Research Articles

Density of states effects on emission and scattering of photons in plasmas

Plasma supports electromagnetic waves propagation for frequencies higher than plasma frequency but features dielectric permittivity less than 1. This property leads to photon density of states (DOS) lower than in vacuum and should result in subnatural spectral linewidths, sub-Planckian spectrum of thermal radiation, and sub-Rayleigh scattering as well as in lower inelastic photon scattering including Raman scattering. Lamb shift will be altered as well though the decisive contribution from high-energy modes in this case makes the photon DOS effect rather small since plasma DOS converges with the vacuum one in the limit of infinite frequencies. We emphasize the basic character of all these phenomena though absolute values of corrections in many real experiments may appear to be small as compared to other factors. We found that dissipative losses make possible DOS effects smaller though not vanishing and additionally bring about indefinite growth of DOS in the low-frequency limit.

Large Single-Phonon Optomechanical Coupling Between Quantum Dots and Tightly Confined Surface Acoustic Waves in the Quantum Regime

Surface acoustic waves (SAWs) coupled to quantum dots (QDs), trapped atoms and ions, and point defects have been proposed as quantum transduction platforms, yet the requisite coupling rates and cavity lifetimes have not been experimentally established. Although the interaction mechanism varies, small acoustic cavities with large zero-point motion are required for high efficiencies. We experimentally establish the feasibility of this platform through electro- and optomechanical characterization of tightly focusing, single-mode Gaussian SAW cavities at approximately 3.6 GHz on $\mathrm{Ga}\mathrm{As}$. We explore the performance limits of the platform by fabricating SAW cavities with mode volumes approaching $6{\ensuremath{\lambda}}^{3}$ and linewidths less than 1 MHz. Employing strain-coupled single $\mathrm{In}\mathrm{As}$ QDs as optomechanical intermediaries, we measure single-phonon optomechanical coupling rates ${g}_{0}\ensuremath{\approx}2\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}1.2$ MHz. Sideband scattering rates thus exceed intrinsic phonon loss, indicating the potential for quantum optical readout and transduction of cavity phonon states. To demonstrate the feasibility of this platform for low-noise ground-state quantum transduction, we develop a fiber-based confocal microscope in a dilution refrigerator and perform single-QD resonance fluorescence sideband spectroscopy at millikelvin temperatures. These measurements show conversion between microwave phonons and optical photons with sub-natural linewidths.

Density of States Effects on Emission and Scattering of Photons in Plasmas

Plasma supports electromagnetic waves propagation for frequencies higher than plasma frequency but features dielectric permittivity less than 1. This property leads to photon density of states (DOS) lower than in vacuum and should result in subnatural spectral linewidths, sub-Planckian spectrum of thermal radiation, and in sub-Rayleigh photon scattering as well as in lower inelastic photon scattering including Raman scattering in molecular and crystalline structures. We emphasize the basic character of these phenomena though absolute values of corrections from this property of plasmas in many real experiments may appear to be small as compared to other factors. We found that dissipative losses when being taken into account make possible DOS effects smaller though not vanishing and additionally bring about indefinite growth of DOS in the low-frequency limit.

Driving-induced population trapping and linewidth narrowing via the quantum Zeno effect

We investigate the suppression of spontaneous emission from a driven three-level system embedded in an optical cavity via a manifestation of the quantum Zeno effect. Strong resonant coupling of the lower two levels to an external optical field results in a decrease of the exponential decay rate of the third upper level. We show that this effect has observable consequences in the form of emission spectra with subnatural linewidths, which should be measurable using, for example, quantum dot--cavity systems in currently obtainable parameter regimes. These results constitute a novel method to control an inherently irreversible and dissipative process, and may be useful in applications requiring the control of single photon arrival times and wavepacket extent.

Sub-megahertz linewidth single photon source

We report 100% duty cycle generation of sub-MHz single photon pairs at the rubidium D1 line using cavity-enhanced spontaneous parametric downconversion. The temporal intensity cross correlation function exhibits a bandwidth of 666±16 kHz for the single photons, an order of magnitude below the natural linewidth of the target transition. A half-wave plate inside our cavity helps to achieve triple resonance between pump, signal, and idler photon, reducing the bandwidth and simplifying the locking scheme. Additionally, stabilisation of the cavity to the pump frequency enables the 100% duty cycle. The quantum nature of the source is confirmed by the idler-triggered second-order autocorrelation function at τ=0 to be gs,s(2)(0)= 0.016±0.002 for a heralding rate of 5 kHz. The generated photons are well-suited for storage in quantum memory schemes with sub-natural linewidths, such as gradient echo memories.

Coherent control of group index and magneto-optical anisotropy in a multilevel atomic vapor.

We study electromagnetically induced transparency (EIT) in a heated potassium vapor cell, using a simple optical setup with a single free-running diode laser and an acousto-optic modulator. Despite the fact that the Doppler width is comparable to the ground state hyperfine splitting, transparency windows with deeply sub-natural line widths and large group indices are obtained. A longitudinal magnetic field is used to split the EIT feature and induce magneto-optical anisotropy. Using the beat note between co-propagating coupling and probe beams, we perform a heterodyne measurement of the circular dichroism (and therefore birefringence) of the EIT medium. The observed spectra reveal that lin‖lin polarizations lead to greater anisotropy than lin⊥lin. A simplified ‖analytical model encompassing sixteen Zeeman states and eighteen Λ subsytems reproduces the experimental observations.

Subnatural linewidths in two-photon excited-state spectroscopy

We investigate, theoretically and experimentally, absorption on an excited-state atomic transition in a thermal vapor where the lower state is coherently pumped. We find that the transition linewidth can be sub-natural, i.e. less than the combined linewidth of the lower and upper state. For the specific case of the 6P_{3/2} -> 7S_{1/2} transition in room temperature cesium vapor, we measure a minimum linewidth of 6.6 MHz compared with the natural width of 8.5 MHz. Using perturbation techniques, an expression for the complex susceptibility is obtained which provides excellent agreement with the measured spectra.

Probing the Spontaneous Emission Dynamics in Si-Nanocrystals-Based Microdisk Resonators

As a possible cavity quantum electrodynamical system, unlike III-V quantum dots, Si-NCs are not considered ideal emitters for emission rate enhancement observations (Purcell effect). Here, we report on direct measurements of spontaneous emission rate enhancement of Si-NCs embedded in a whispering-gallery mode resonator at room temperature. Using time-resolved microphotoluminescence experiments, we demonstrate important lifetime reductions (approximately 70%) for Si-NCs coupled to cavity modes with respect to uncoupled ones. Comparing experiments with the theoretical Purcell enhancement in a bad emitter regime, we estimate effective linewidths of approximately 10 meV through which Si-NC emitters are coupled to cavity photons. Finally, our study provides an alternative method for the estimation of subnatural linewidths of quantum dots at room temperature.

Normal-mode splitting with large collective cooperativity

We report the observation of normal-mode splitting of the atom-cavity dressed states in both the fluorescence and transmission spectra for large atom number and observe subnatural linewidths in this regime. We also implement a method of utilizing the normal-mode splitting to observe Rabi oscillations on the $^{87}\mathrm{Rb}$ ground state hyperfine clock transition. We demonstrate a large collective cooperativity, $C=1.2\ifmmode\times\else\texttimes\fi{}{10}^{4}$, which, in combination with large atom number, $N\ensuremath{\sim}2\ifmmode\times\else\texttimes\fi{}{10}^{5}$, offers the potential to realize an absolute phase sensitivity better than that achieved by state-of-the-art atomic fountain clocks or inertial sensors operating near the quantum projection noise limit.

Thirteen pump-probe resonances of the sodiumD1line

We present the results of a pump-probe laser spectroscopic investigation of the Doppler-broadened sodium $D1$ resonance line. We find 13 resonances in the resulting spectra. These observations are well described by the numerical predictions of a four-level atomic model of the hyperfine structure of the sodium $D1$ line. We also find that many, but not all, of these features can be understood in terms of processes originating in a two-level or three-level subset of the full four-level model. The processes we observed include forward near-degenerate four-wave mixing and saturation in a two-level system, difference-frequency crossing and nondegenerate four-wave mixing in a three-level V system, electromagnetically induced transparency and optical pumping in a three-level lambda system, cross-transition resonance in a four-level double-lambda system, and conventional optical pumping. Most of these processes lead to sub-Doppler or even subnatural linewidths. The dependence of these resonances on the pump intensity and pump detuning from atomic resonance are also studied.

Two-photon interference spectra at the sum-frequency generation of a bichromatic field interacting with a three-level atom

We have calculated the spectral functions for a number of induced excitations near the sum-frequency generation of a bichromatic field interacting with a three-level atom in the cascade configuration. Although the two-photon spontaneous emission is electric dipole forbidden, there are induced peaks whose subnatural line widths and spectral heights depend on the intensities of the bichromatic field. At low intensities of both laser fields, the maximum heights of the induced peaks take positive, zero, and negative values, indicating that the physical processes of absorption (attenuation), dark resonance (nonabsorbing state), and stimulated emission (amplification) are likely to occur at the sum-frequency generation of the two laser fields, respectively. The derived results are graphically presented and discussed.

Quantum interference spectra at the difference-frequency generation in four-level atomic systems

Analytical expressions of the spectral functions have been derived for a number of induced excitations that occur near the difference-frequency generation in a four-level atomic system interacting with three laser fields. The spectral heights and subnatural line widths of the induced peaks depend on the intensities of the laser fields involved. The maximum heights of the induced peaks take positive, zero and negative values, indicating that the processes of absorption (attenuation), dark resonance and stimulated emission (amplification) are likely to occur near the difference-frequency generation, respectively.

Electromagnetically induced gratings in a degenerate open two-level system

We have experimentally investigated laser diffraction on electromagnetically induced gratings in a degenerate open two-level system. The experiment employs the standard backward four-wave mixing configuration and the open ${6S}_{1/2}(F=4)\ensuremath{\rightarrow}{6P}_{3/2}{(F}^{\ensuremath{'}}=4)$ transition of cold cesium atoms. Population and coherence gratings are accessed for different relative polarizations of the incident laser beams. Natural and subnatural linewidths are observed depending on which frequency of the incident beams is scanned and reveal the effect of the atomic motion on the diffraction spectra. A simple theoretical model using a three-level $\ensuremath{\Lambda}$ system is in reasonable agreement with the observed results and allowed us to make a close connection with the phenomenon of electromagnetically induced transparency.

Phase-dependent fluorescence linewidth narrowing in a three-level atom damped by a finite-bandwidth squeezed vacuum

We examine subnatural phase-dependent linewidths in the fluorescence spectrum of a three-level atom damped by a narrow-bandwidth squeezed vacuum in a cavity. Using the dressed-atom model approach of a strongly driven three-level cascade system, we derive the master equation of the system from which we obtain simple analytical expressions for the fluorescence spectrum. We show that the phase effects depend on the bandwidths of the squeezed vacuum and the cavity relative to the Rabi frequency of the driving fields. When the squeezing bandwidth is much larger than the Rabi frequency, the spectrum consists of five lines with only the central and outer sidebands dependent on the phase. For a squeezing bandwidth much smaller than the Rabi frequency the number of lines in the spectrum and their phase properties depend on the frequency at which the squeezing and cavity modes are centered. When the squeezing and cavity modes are centered on the inner Rabi sidebands, the spectrum exhibits five lines that are completely independent of the squeezing phase with only the inner Rabi sidebands dependent on the squeezing correlations. Matching the squeezing and cavity modes to the outer Rabi sidebands leads to the disappearance of the inner Rabi sidebands and a strong phase dependence of the central line and the outer Rabi sidebands. We find that in this case the system behaves as an individual two-level system that reveals exactly the noise distribution in the input squeezed vacuum.

Assignment of fine structure in the HBr absorption spectrum at the Br3d→Rydberg resonances using the Auger resonant Raman effect

High-resolution resonant Auger electron spectra of HBr are reported at the Br $3d\ensuremath{\rightarrow}5p$ and Br $3d\ensuremath{\rightarrow}4d$ resonances. Subnatural linewidths of \ensuremath{\sim}40 meV, due to the Auger resonance Raman effect, reveal complex multiplet features. By recording spectra at closely spaced energies, the resonant Auger spectra from the resonantly excited core Br $3d$ to $4d,$ $5p\ensuremath{\sigma},$ and $5p\ensuremath{\pi}$ Rydberg states are obtained. The well-resolved resonant Auger spectra are used to confirm the assignments of the complex unresolved Br $3d\ensuremath{\rightarrow}$Rydberg photoabsorption spectrum.

Control-laser-induced subnatural linewidths and quenching of spontaneous emission.

We show how control lasers lead to subnatural linewidths in spontaneous emission as well as to the quenching of the quantum noise. We trace this quenching to the dispersive contributions to the line shape. We obtain analytical expressions for linewidths that for $\ensuremath{\wedge}$ systems are half the natural linewidths with the possibility of much more reduction for detuned control laser. We further present a simple physical analysis in terms of a two-photon Fermi golden rule to understand cancellation of spontaneous emission. Finally, we relate our results to recent experiments.

The asymptotic behaviour of the spectrum of resonance fluorescence

Abstract The spectrum of resonance fluorescence from laser-driven multi-level systems is investigated and especially its asymptotic frequency dependence in the wings. Analytical results are presented and the transitions within multilevel systems are classified into three categories according to the asymptotic frequency dependence of their spectra. Under certain conditions an arbitrarily fast asymptotic fall-off behaviour of the spectrum is found which, for intermediately strong driving fields, leads to subnatural linewidths. Numerical examples are presented to illustrate the analytical results.

Influence of squeezing bandwidths on resonance fluorescence

Abstract We present an analytical technique for investigating the behaviour of a coherently driven atom damped by a squeezed vacuum with finite squeezing bandwidth. A master equation and analytic expressions for the fluorescent spectrum are derived for the simple case of a two-level atom exactly resonant with the frequencies of both the squeezed field and the driving field. Suitable choices of driving strength, phase and squeezing source lead to either sub-natural lincwidths of the Rabi sidebands or a sub-natural linewidth of the central spectral peak or indeed sub-natural linewidths of all three spectral peaks when squeezing bandwidths are taken into account. We also establish the remarkable result that in the strong driving regime, the width of the central peak of the fluorescent spectrum depends solely on the squeezing found at the Rabi sideband frequencies.

Influence of squeezing bandwidths on resonance fluorescence

Abstract We present an analytical technique for investigating the behaviour of a coherently driven atom damped by a squeezed vacuum with finite squeezing bandwidth. A master equation and analytic expressions for the fluorescent spectrum are derived for the simple case of a two-level atom exactly resonant with the frequencies of both the squeezed field and the driving field. Suitable choices of driving strength, phase and squeezing source lead to either sub-natural lincwidths of the Rabi sidebands or a sub-natural linewidth of the central spectral peak or indeed sub-natural linewidths of all three spectral peaks when squeezing bandwidths are taken into account. We also establish the remarkable result that in the strong driving regime, the width of the central peak of the fluorescent spectrum depends solely on the squeezing found at the Rabi sideband frequencies.

Observation of strongly subhomogeneous linewidths using high-contrast transmission spectroscopy: Experiment and theory.

Several papers have recently addressed the issue of ob- taining subnatural linewidth and subnatural resolution by performing Doppler-free spectroscopy on samples of high optical density ~so-called high-contrast transmission spec- troscopy !@ 1-7#. In this paper we experimentally and theo- retically demonstrate that lines with strongly subnatural linewidths can be obtained using high-contrast transmission spectroscopy ~HCTS!. Linewidths close to half the natural linewidth are obtained by using the so-called ''tandem ar- rangement'' @2 #@ standard and ''tandem'' experimental con- figurations are schematically shown in Figs. 1~a! and 1~b! respectively#. In the latter configuration the Doppler-free out- put signal from a saturation spectroscopy measurement on a high optical density cell is used as the input light source for a Doppler-free saturation spectroscopy measurement in a second cell, which also is of high optical density. Due to the line-narrowing effect of HCTS the Doppler-free output sig- nal from this second cell may have a linewidth substantially lower than the natural linewidth. The observed line narrowing is explained and supported by theoretical calculations. The theoretical modeling is based on rate equations specifically including velocity-selective op- tical pumping. Previous theoretical analyses have included rate equations @2,7# as well as optical Bloch equations @3-6 #. The present experiment and calculations have been per- formed on the 3s 2 S 1/2 -3 p 2 P 1/2 transition in sodium. We will briefly describe the prerequisites for the calculations. The coupling of the total angular momentum with the nuclear spin of I5 3 2 turns this transition into a four-level system ~neglecting the Zeeman degeneracy! with total angu- lar momentum F51 and F52 in the upper as well as lower electronic state. The optically induced transparency is then caused by velocity-selective optical pumping between the two ground-state hyperfine levels. At sample temperatures below 200 °C the mean free path of the sodium atoms is.1 m. This means that redistribution of optically hyperfine pumped atoms essentially then only occurs when the atoms collide with the walls of the cell and other collision pro- cesses can be neglected. An atomic velocity of 600 m/s per- pendicular to the laser beam and a 2-mm-diameter beam yields a transit time through the beam for the atoms of about 3 ms. This consequently would more or less be the average time until an optically pumped atom is replaced by an un- pumped atom. With an upper state lifetime of 16 ns the tran- sit time through the beam is much longer than any coherence between the ground and excited state. Although use of the