Natural Linewidth Research Articles

Erratum: Narrow dip inside a natural linewidth absorption profile in a system of two atoms [Phys. Rev. A92, 053840 (2015)

Erratum: Narrow dip inside a natural linewidth absorption profile in a system of two atoms [Phys. Rev. A92, 053840 (2015)

Subnatural-linewidth biphotons from a Doppler-broadened hot atomic vapour cell.

Entangled photon pairs, termed as biphotons, have been the benchmark tool for experimental quantum optics. The quantum-network protocols based on photon–atom interfaces have stimulated a great demand for single photons with bandwidth comparable to or narrower than the atomic natural linewidth. In the past decade, laser-cooled atoms have often been used for producing such biphotons, but the apparatus is too large and complicated for engineering. Here we report the generation of subnatural-linewidth (<6 MHz) biphotons from a Doppler-broadened (530 MHz) hot atomic vapour cell. We use on-resonance spontaneous four-wave mixing in a hot paraffin-coated 87Rb vapour cell at 63 °C to produce biphotons with controllable bandwidth (1.9–3.2 MHz) and coherence time (47–94 ns). Our backward phase-matching scheme with spatially separated optical pumping is the key to suppress uncorrelated photons from resonance fluorescence. The result may lead towards miniature narrowband biphoton sources.

A single-mode external cavity diode laser using an intra-cavity atomic Faraday filter with short-term linewidth

We report on the development of a diode laser system - the "Faraday laser" - using an atomic Faraday filter as the frequency-selective element. In contrast to typical external-cavity diode laser systems which offer tunable output frequency but require additional control systems in order to achieve a stable output frequency, our system only lases at a single frequency, set by the peak transmission frequency of the internal atomic Faraday filter. Our system has both short-term and long-term stability of less than 1 MHz, which is less than the natural linewidth of alkali-atomic D-lines, making similar systems suitable for use as a "turn-key" solution for laser-cooling experiments.

Inner-shell magnetic dipole transition in Tm atoms: A candidate for optical lattice clocks

We consider a narrow magneto-dipole transition in the $^{169}$Tm atom at the wavelength of $1.14\,\mu$m as a candidate for a 2D optical lattice clock. Calculating dynamic polarizabilities of the two clock levels $[\text{Xe}]4f^{13}6s^2 (J=7/2)$ and $[\text{Xe}]4f^{13}6s^2 (J=5/2)$ in the spectral range from $250\,$nm to $1200\,$nm, we suggest the "magic" wavelength for the optical lattice at $807\,$nm. Frequency shifts due to black-body radiation (BBR), the van der Waals interaction, the magnetic dipole-dipole interaction and other effects which can perturb the transition frequency are calculated. The transition at $1.14\,\mu$m demonstrates low sensitivity to the BBR shift corresponding to $8\times10^{-17}$ in fractional units at room temperature which makes it an interesting candidate for high-performance optical clocks. The total estimated frequency uncertainty is less than $5 \times 10^{-18}$ in fractional units. By direct excitation of the $1.14\,\mu$m transition in Tm atoms loaded into an optical dipole trap, we set the lower limit for the lifetime of the upper clock level $[\text{Xe}]4f^{13}6s^2 (J=5/2)$ of $112\,$ms which corresponds to a natural spectral linewidth narrower than $1.4\,$Hz. The polarizability of the Tm ground state was measured by the excitation of parametric resonances in the optical dipole trap at $532\,$nm.

Spectroscopic probe of the van der Waals interaction between polar molecules and a curved surface

We study the shift of rotational levels of a diatomic polar molecule due to its van der Waals (vdW) interaction with a gently curved dielectric surface at temperature $T$, and submicron separations. The molecule is assumed to be in its electronic and vibrational ground state, and the rotational degrees are described by a rigid rotor model. We show that under these conditions retardation effects and surface dispersion can be neglected. The level shifts are found to be independent of $T$, and given by the quantum state averaged classical electrostatic interaction of the dipole with its image on the surface. We use a derivative expansion for the static Green's function to express the shifts in terms of surface curvature. We argue that the curvature induced line splitting is experimentally observable, and not obscured by natural line widths and thermal broadening.

Pronounced Surface Band Bending of Thin-Film Silicon Revealed by Modeling Core Levels Probed with Hard X-rays.

Enhancing the probing depth of photoemission studies by using hard X-rays allows the investigation of buried interfaces of real-world device structures. However, it also requires the consideration of photoelectron-signal attenuation when evaluating surface effects. Here, we employ a computational model incorporating surface band bending and exponential photoelectron-signal attenuation to model depth-dependent spectral changes of Si 1s and Si 2s core level lines. The data were acquired from hydrogenated boron-doped microcrystalline thin-film silicon, which is applied in silicon-based solar cells. The core level spectra, measured by hard X-ray photoelectron spectroscopy using different excitation energies, reveal the presence of a 0.29 nm thick surface oxide layer. In the silicon film a downward surface band bending of eVbb = -0.65 eV over ∼6 nm obtained via inverse modeling explains the observed core level shifts and line broadening. Moreover, the computational model allows the extraction of the "real" Si 1s and Si 2s bulk core level binding energies as 1839.13 and 150.39 eV, and their natural Lorentzian line widths as 496 and 859 meV, respectively. These values significantly differ from those directly extracted from the measured spectra. Because band bending usually occurs at material surfaces we highly recommend the detailed consideration of signal integration over depth for quantitative statements from depth-dependent measurements.

On the nonlinear theory of Fabry–Perot semiconductor lasers

Fundamentals of the nonlinear theory of Fabry–Perot semiconductor lasers have been developed, an integral part of which is natural linewidth theory. The formula for gain depending on the energy flux specifies the basic nonlinear effect in a laser. Necessary conditions for stimulated emission of the first and second kind are presented. Maxwell’s equations in the gain medium are applied to obtain equations for energy flux and for the description of non-linear phase effect. Based on the nonlinear theory, a number of experiments have been simulated; it indicates that the nonlinear theory is a new paradigm in laser theory. The nonlinear theory has provided recommendations for the development of lasers with improved properties, such as lasers with increased power and lasers with reduced natural linewidth.

Collective atomic scattering and motional effects in a dense coherent medium.

We investigate collective emission from coherently driven ultracold 88Sr atoms. We perform two sets of experiments using a strong and weak transition that are insensitive and sensitive, respectively, to atomic motion at 1 μK. We observe highly directional forward emission with a peak intensity that is enhanced, for the strong transition, by >103 compared with that in the transverse direction. This is accompanied by substantial broadening of spectral lines. For the weak transition, the forward enhancement is substantially reduced due to motion. Meanwhile, a density-dependent frequency shift of the weak transition (∼10% of the natural linewidth) is observed. In contrast, this shift is suppressed to <1% of the natural linewidth for the strong transition. Along the transverse direction, we observe strong polarization dependences of the fluorescence intensity and line broadening for both transitions. The measurements are reproduced with a theoretical model treating the atoms as coherent, interacting radiating dipoles.

Evaluating and overcoming the impact of second echo in Brillouin echoes distributed sensing.

The detrimental impact of the second echo phenomenon that commonly exists in Brillouin echoes distributed sensing (BEDS) methods is thoroughly investigated by further developing the analytical model of the Brillouin gain on the probe wave. The presented analysis not only points out that the most severe impact imposed by the second echo occurs when the length of the heated/stressed fiber section is exactly equal to the spatial resolution, but also quantifies the systematic error on the estimated Brillouin frequency shift, the maximum of which could reach up to 8.5 MHz. A novel parabolic-amplitude four-section pulse is proposed, which can compensate the impact of the second echo optically, without using extra measurement time and post-processing. The key parameters of the proposed pulse are optimized by combining an upgraded mathematical model and the iterative algorithm. The experimental results show a good agreement with the analysis about the behavior of the second echo, and demonstrate that the proposed technique is capable of providing sub-meter spatial resolution and the natural linewidth of Brillouin gain spectrum simultaneously, while completely eliminating the impact of the second echo.

Detection of motional ground state population of a trapped ion using delayed pulses

Efficient preparation and detection of the motional state of trapped ions is important in many experiments ranging from quantum computation to precision spectroscopy. We investigate the stimulated Raman adiabatic passage (STIRAP) technique for the manipulation of motional states in a trapped ion system. The presented technique uses a Raman coupling between two hyperfine ground states in 25Mg+, implemented with delayed pulses, which removes a single phonon independent of the initial motional state. We show that for a thermal probability distribution of motional states the STIRAP population transfer is more efficient than a stimulated Raman Rabi pulse on a motional sideband. In contrast to previous implementations, a large detuning of more than 200 times the natural linewidth of the transition is used. This approach renders STIRAP suitable for atoms in which resonant laser fields would populate nearby fluorescing excited states and thus impede the STIRAP process. We use the technique to measure the wavefunction overlap of excited motional states with the motional ground state. This is an important application for force sensing applications using trapped ions, such as photon recoil spectroscopy, in which the signal is proportional to the depletion of motional ground state population. Furthermore, a determination of the ground state population enables a simple measurement of the ion's temperature.

Time-delayed intensity–interferometry of the emission from ultracold atoms in a steady-state magneto-optical trap

Time-delayed intensity–interferometry (TDII) measurements of the fluorescent emission from an ultracold ensemble of thermal 87Rb atoms in a steady-state magneto-optical trap are presented, which reveal the underlying coherent and incoherent dynamics of the atoms. Measurements carried out with a 5 ns time resolution yielded a second-order intensity correlation function with the theoretically predicted value of 2 at zero delay. In addition coherent Rabi oscillations were seen for up to five full periods—much longer than the spontaneous emission lifetime of the excited state of Rb. The oscillations were damped out by ∼150 ns, and thereafter an exponential decay observed, from which the mean velocity of atoms and thus, the temperature of the ensemble was estimated. The values so obtained compare well with those determined by standard techniques. It is seen that TDII permits a quantitative study of the coherent and incoherent processes, even in a large ensemble of independent atomic emitters in random thermal motion. This measurement of second-order correlation powerful technique can reveal hidden periodicities such as coherent Rabi oscillations that are not directly seen in the emission from a large collection of atoms. In addition it can also reveal information about the mean velocity of the thermal ensemble of emitters, even though the Doppler broadening of emission due to the motion of atoms is smaller than the natural linewidth and is not directly measureable.

A General Method for Extracting Individual Coupling Constants from Crowded 1H NMR Spectra

AbstractCouplings between protons, whether scalar or dipolar, provide a wealth of structural information. Unfortunately, the high number of 1H‐1H couplings gives rise to complex multiplets and severe overlap in crowded spectra, greatly complicating their measurement. Many different methods exist for disentangling couplings, but none approaches optimum resolution. Here, we present a general new 2D J‐resolved method, PSYCHEDELIC, in which all homonuclear couplings are suppressed in F2, and only the couplings to chosen spins appear, as simple doublets, in F1. This approaches the theoretical limit for resolving 1H‐1H couplings, with close to natural linewidths and with only chemical shifts in F2. With the same high sensitivity and spectral purity as the parent PSYCHE pure shift experiment, PSYCHEDELIC offers a robust method for chemists seeking to exploit couplings for structural, conformational, or stereochemical analyses.

A General Method for Extracting Individual Coupling Constants from Crowded (1)H NMR Spectra.

Couplings between protons, whether scalar or dipolar, provide a wealth of structural information. Unfortunately, the high number of 1H‐1H couplings gives rise to complex multiplets and severe overlap in crowded spectra, greatly complicating their measurement. Many different methods exist for disentangling couplings, but none approaches optimum resolution. Here, we present a general new 2D J‐resolved method, PSYCHEDELIC, in which all homonuclear couplings are suppressed in F 2, and only the couplings to chosen spins appear, as simple doublets, in F 1. This approaches the theoretical limit for resolving 1H‐1H couplings, with close to natural linewidths and with only chemical shifts in F 2. With the same high sensitivity and spectral purity as the parent PSYCHE pure shift experiment, PSYCHEDELIC offers a robust method for chemists seeking to exploit couplings for structural, conformational, or stereochemical analyses.

The realization of the dipole (γ, γ) method and its application to determine the absolute optical oscillator strengths of helium.

The dipole (γ, γ) method, which is the inelastic x-ray scattering operated at a negligibly small momentum transfer, is proposed and realized to determine the absolute optical oscillator strengths of the vanlence-shell excitations of atoms and molecules. Compared with the conventionally used photoabsorption method, this new method is free from the line saturation effect, which can seriously limit the accuracies of the measured photoabsorption cross sections for discrete transitions with narrow natural linewidths. Furthermore, the Bethe-Born conversion factor of the dipole (γ, γ) method varies much more slowly with the excitation energy than does that of the dipole (e, e) method. Absolute optical oscillator strengths for the excitations of 1s2 → 1 snp(n = 3 − 7) of atomic helium have been determined using the high-resolution dipole (γ, γ) method, and the excellent agreement of the present measurements with both those measured by the dipole (e, e) method and the previous theoretical calculations indicates that the dipole (γ, γ) method is a powerful tool to measure the absolute optical oscillator strengths of the valence-shell excitations of atoms and molecules.

Excitonic fine structure splitting in type-II quantum dots

Excitonic fine structure splitting in quantum dots is closely related to the lateral shape of the wave functions. We have studied theoretically the fine structure splitting in InAs quantum dots with a type-II confinement imposed by a GaAsSb capping layer. We show that very small values of the fine structure splitting comparable with the natural linewidth of the excitonic transitions are achievable for realistic quantum dots despite the structural elongation and the piezoelectric field. For example, varying the capping layer thickness allows for a fine tuning of the splitting energy. The effect is explained by a strong sensitivity of the hole wave function to the quantum dot structure and a mutual compensation of the electron and hole anisotropies. The oscillator strength of the excitonic transitions in the studied quantum dots is comparable to those with a type-I confinement which makes the dots attractive for quantum communication technology as emitters of polarization-entangled photon pairs.

Narrow dip inside a natural linewidth absorption profile in a system of two atoms

Absorption spectrum of a system of two closely spaced identical atoms displays, at certain preparation, a dip that can be much narrower than the natural linewidth. This preparation includes (i) application of a strong magnetic field at an angle $\ensuremath{\alpha}$, that is very close to the magic angle ${\ensuremath{\alpha}}_{0}=arccos(1/\sqrt{3})\ensuremath{\approx}{54.7}^{\ensuremath{\circ}}$, with respect to the direction from one atom to another, and (ii) in-plane illumination by a laser light in the form of a nonresonant standing wave polarized at the same angle $\ensuremath{\alpha}$. Both qualitative and quantitative arguments for the narrow dip effect are presented.

Conservation laws and laser cooling of atoms

The straightforward application of energy and linear momentum conservation to the absorption/emission of photons by atoms allows us to establish the essential features of laser cooling of two level atoms at low laser intensities. The lowest attainable average kinetic energy of the atoms depends on the ratio between the natural linewidth and the recoil energy and tends to ER as tends to zero (in one dimension). This treatment, like the quantum mechanical ones, is valid for any value of the ratio and contains the semiclassical theory of laser cooling as the limiting case in which .

Investigations of the Zeeman effect of some 142Nd ionic levels, using collinear laser ion beam spectroscopy

By performing laser excitation from the even 4f45d lower levels to the odd 4f46p and 4f35d2 upper levels of the neodymium ion 142Nd+, we have observed Zeeman splitting in an external magnetic field up to 330G. We applied the high resolution spectroscopic method of collinear laser ion beam spectroscopy (CLIBS). With this method (unconventional for studying the Zeeman effect) we recorded very well-resolved Zeeman structure patterns with line widths of order of 100MHz, which is only sometimes the natural line width. The obtained experimental Landé factors are compared with earlier measurements and with theoretical calculations.

Narrowband polarization entangled paired photons with controllable temporal length

Quantum networks strongly depend on the efficient interactions between flying photonic quantum bits and local long-lived atomic matter nodes. To achieve the efficient quantum interfaces between polarization-encoding photons and spin-encoding atoms, polarization-entangled paired photons with a bandwidth narrower than the natural linewidth of the atoms are highly required. In this paper, we review the generation of subnatural-linewidth polarization-entangled paired photons through spontaneous four-wave mixing with cold atoms, which is very suitable for the application of quantum networks.

14N Quadrupole Resonance line broadening due to the earth magnetic field, occuring only in the case of an axially symmetric electric field gradient tensor

As demonstrated before, the application of a weak static B0 magnetic field (less than 10G) may produce definite effects on the 14N Quadrupole Resonance line when the electric field gradient tensor at the nitrogen nucleus level is of axial symmetry. Here, we address more precisely the problem of the relative orientation of the two magnetic fields (the static field and the radio-frequency field of the pure NQR experiment). For a field of 6G, the evolution of the signal intensity, as a function of this relative orientation, is in very good agreement with the theoretical predictions. There is in particular an intensity loss by a factor of three when going from the parallel configuration to the perpendicular configuration. By contrast, when dealing with a very weak magnetic field (as the earth field, around 0.5G), this effect drops to ca. 1.5 in the case Hexamethylenetetramine (HMT).This is explained by the fact that the Zeeman shift (due to the very weak magnetic field) becomes comparable to the natural line-width. The latter can therefore be determined by accounting for this competition. Still in the case of HMT, the estimated natural line-width is half the observed line-width. The extra broadening is thus attributed to earth magnetic field. The latter constitutes therefore the main cause of the difference between the natural transverse relaxation time (T2) and the transverse relaxation time derived from the observed line-width (T2⁎).