Continuous narrowband lasing with coherently driven V-level atoms

Atoms without ground state splitting, e.g. alkaline earths, are of special interest for atom interferometry and frequency standards due to their small sensitivity to external fields and for BEC and the study of cold collisions due to the simplified theoretical interpretation of their interaction. We demonstrate Maxwell's-demon cooling, a novel method which allows to further cool alkaline earth atoms in one dimension. It consists of three consecutive steps which are repeated several times. First, from a cloud of cooled atoms released from a standard magneto-optical trap a small part of the velocity distribution is selected by excitation on a narrow transition (intercombination transition). Second, these atoms are optically pumped to another long lived state. Third, the ground state velocity distribution is restored by turning on the optical molasses on the strong transition used for the magneto-optical trapping. In addition to Maxwell's thought experiment, where a demon separates the cold atoms from the hot ones, in the novel scheme the hot atoms are furthermore cooled again to the original 3 mK. By repeating these steps slow atoms are accumulated in the excited state. The velocity distribution of the atoms is measured after the cold atoms are decayed to the ground state by recording the Doppler broadening of the intercombination transition.

When a pump field and probe field simultaneously drive an electronic-state atomic transition, the probe field absorption spectrum can consist of an absorption peak centered near \ensuremath{\Delta}'=0 and amplification peak centered near \ensuremath{\Delta}'=2\ensuremath{\Delta} (\ensuremath{\Delta} and \ensuremath{\Delta}' are the pump and probe field detunings from the atomic transition frequency, respectively). This type of spectrum is seen in the limit \ensuremath{\Vert}\ensuremath{\Delta}\ensuremath{\Vert}\ensuremath{\gg}\ensuremath{\chi}\ensuremath{\gg}\ensuremath{\Gamma}, where \ensuremath{\chi} is the Rabi frequency associated with the pump field and 2\ensuremath{\Gamma} is the homogeneous width associated with the atomic transition. For atoms cooled below the recoil limit of laser cooling, the qualitative nature of the probe absorption spectrum can undergo a dramatic change. Provided that the recoil splitting ${\mathrm{\ensuremath{\omega}}}_{\mathit{k}}$ is larger than the homogeneous decay rate (as might occur in the case of a forbidden transition), the absorption and amplification features each split into an absorption-amplification doublet. In addition, structure is found in the probe absorption spectrum near \ensuremath{\Delta}'=\ensuremath{\Delta}; this structure consists of two absorption-amplification doublets. Both doublets can be resolved if ${\mathrm{\ensuremath{\omega}}}_{\mathit{k}}$>\ensuremath{\Gamma}. If ${\mathrm{\ensuremath{\omega}}}_{\mathit{k}}$, one of the doublets can be resolved provided that ${\mathrm{\ensuremath{\omega}}}_{\mathit{k}}$>${\mathrm{\ensuremath{\Gamma}}}_{\mathit{A}}$, where ${\mathrm{\ensuremath{\Gamma}}}_{\mathit{A}}$ is some effective atomic ground state width in the problem. The positions, widths, and relative weights of all the components are readily predicted using a dressed-atom theory in which quantization of the center-of-mass momentum is included. An analytical expression for the probe field spectrum is obtained for a simple case in which spontaneous decay to the lower level is neglected. Validity criteria for the results are discussed.

Theories unifying gravity with other interactions suggest spatial and temporal variation of fundamental “constants” in the Universe. A change in the fine structure constant, $$\alpha = {e}^{2}/\hslash c$$ , could be detected via shifts in the frequencies of atomic transitions in quasar absorption systems. Recent studies using 140 absorption systems from the Keck telescope and 153 from the Very Large Telescope, suggest that α varies spatially (61). That is, in one direction on the sky α seems to have been smaller at the time of absorption, while in the opposite direction it seems to have been larger. To continue this study we need accurate laboratory measurements of atomic transition frequencies. The aim of this paper is to provide a compilation of transitions of importance to the search for α variation. They are E1 transitions to the ground state in several different atoms and ions, with wavelengths ranging from around 900–6000 Å, and require an accuracy of better than 10 − 4 Å. We discuss isotope shift measurements that are needed in order to resolve systematic effects in the study. The coefficients of sensitivity to α-variation (q) are also presented.

We demonstrate an approach to create a stable erbium-fiber-based frequency comb at communication band by directly locking the combs to two rubidium atomic transitions resonances (electromagnetically induced transparency absorption and two-photon absorption), respectively. This approach directly transfers the precision and stability of the atomic transitions to the comb. With its distinguishing feature of compactness by removing the conventional octave-spanning spectrum and f-to-2f beating facilities and the ability to directly control the comb's frequency at the atomic transition frequency, this stable optical comb can be widely used in optical communication, frequency standard, and optical spectroscopy and microscopy.

Coherent population beating (CPB) phenomenon occurs in a typical three-level system. When the frequency difference between two coherent pumping laser fields has a certain detuning from the ground-state hyperfine splitting, the excited state population will experience a transient oscillation before reaching equilibrium, and the oscillation frequency is equal to the detuning. The CPB phenomenon enables us to directly obtain the beat frequency between the measured radio frequency (RF) signal and the atomic transition frequency. Then we can get the standard frequency by compensating the beat frequency to the RF. We propose a scheme to implement atomic clock based on the CPB phenomenon in 2009, and the scheme has been implemented. When this effect is used to achieve an atomic clock, the frequency stability is directly related to the amplitude and SNR (signal to noise ratio) of the CPB signal. Influence of the ground-state hyperfine sublevels' coherence on CPB signal is theoretically simulated and experimentally investigated in this paper. A formula of the CPB signal is derived by using the semi-classical model of the interaction of atoms with light, and the theoretical simulation is done using the formula obtained. In the experiment two coherent pumping laser fields are used to interact with 87Rb atoms. A CPB process includes the coherence build-up and the CPB stimulation. The coherence of the ground-state hyperfine sublevels is achieved by controlling the pumping time of the coherent laser fields that are resonant to the ground-state hyperfine sublevels. With this method, the relationship between CPB signal and coherence of the ground-state hyperfine sublevels can be observed. Result shows that the amplitude of CPB signal is proportional to the ground-state hyperfine sublevels' coherence. The hign quality CPB signal can be achieved when the CPB stimulation is started with a pure coherent population trapping (CPT) state. In the CPB process, the coherence build-up rate is approximately equal to the coherence decay rate. So a 50% duty cycle square wave can be used to modulate the RF, and the period of the square wave had better be twice of the decay time of the ground-state hyperfine sublevels' coherence. To improve the SNR of CPB signal and the stability of atomic frequency standard, the ground-state hyperfine sublevels' coherence must be built up, improved, and maintained before the CPB stimulation. The feasibility of applying CPB phenomenon to the weak magnetic field measurement and other applications is also discussed in this paper.

We consider transitions of electron holes (vacancies in otherwise filled shells of atomic systems) in multiply charged ions that, due to level crossing of the holes, have frequencies within the range of optical atomic clocks. Strong E1 transitions provide options for laser cooling and trapping, while narrow transitions can be used for high-precision spectroscopy and tests of fundamental physics. We show that hole transitions can have extremely high sensitivity to α variation and propose candidate transitions that have much larger α sensitivities than any previously seen in atomic systems.

Fock states and coherent states have been widely applied in analyses of quantum-optics experiments. In this paper, the application of a set of basis functions that consist of a product of displaced harmonic-oscillator states for the electromagnetic field and atomic states that are eigenfunctions of the momentum operator will be explored. For the case of a single mode, these states are the exact eigenfunctions in the limiting case where the electromagnetic-field mode frequency is much larger than the atomic transition frequency. This choice of basis functions will be used to analyze the interaction of a nonrelativistic, ``two-level'' atom with a single-frequency, quantized electromagnetic-field mode. Since in this basis the sign of the displacement of the electromagnetic-field state depends on the state of the atom, these new basis wave functions exhibit explicitly some aspects of atom-field correlations that are intrinsically quantum mechanical in nature. The analysis will be performed in the electric-dipole approximation for an atomic system that obeys the \ensuremath{\Delta}m=0 selection rule. The rotating-wave-approximation (RWA) terms cannot be made negligible through judicious choice of the field polarization for this system. The diamagnetic term, ${\mathit{e}}^{2}$${\mathbf{A}}^{2}$/2${\mathit{mc}}^{2}$, which is of the same order of magnitude as the RWA terms, is taken into account exactly by slightly modifying the traditional approach to quantizing the electromagnetic field. In this way the physical effects of the diamagnetic term are absorbed into a new electromagnetic cavity mode frequency.An approximate expression for the combined system's energy eigenvalues is found up to third order in the ratio of one-half the atomic transition frequency to the mode frequency. This expression indicates that inclusion of the RWA terms adds a small ``ripple'' on top of the smoothly varying energy eigenvalues when they are plotted as a function of the atom-field coupling constant. The ripple is interpreted as ``interference'' between two displaced oscillator-field states that represent the unperturbed state. When the Fock states are used as the basis for expanding the wave function of this system, a formidable five-term recurrence relation results. However, expanding the wave function in terms of the displaced harmonic-oscillator basis results in a less formidable three-term recurrence relation for the quantum coefficients.

In general terms the operating principle of the optically pumped gas-cell atomic clock can be described quite simply: an optical field polarizes an atomic ensemble by optical pumping, and additionally monitors the degree of polarization that is attained; simultaneously, the atomic ensemble interacts with a microwave field, which reduces the degree of polarization in the atomic ensemble when the microwave field’s frequency matches an appropriate atomic transition frequency. Specifically, the polarization corresponds to hyperfine polarization in the ground state of an alkali metal vapor (monitored by the level of optical transmission through the vapor, which is confined inside a microwave cavity), and the microwave field is resonant with the alkali’s 0–0 hyperfine transition frequency. Since the measured atomic line Q in this case is quite high (~ 107), the optically detected change in polarization can be used to discriminate against very small microwave field frequency changes, and recent results have shown that stabilities of one part in 1014 can be realized with this device [1]. However, behind this general simplicity is a high degree of complexity, so much so that until recently not even the shot noise limited performance of the device could be theoretically determined with accuracy.

Atomic transitions of Rb, D2 line in strong magnetic fields: Hyperfine Paschen–Back regime

We investigate the storage of light in atomic rubidium vapor using a multilevel-tripod scheme. In the system, two collective dark polariton modes exist, forming an effective spinor quasiparticle. Storage of light is performed by dynamically reducing the optical group velocity to zero. After releasing the stored pulse, a beating of the two reaccelerated optical modes is monitored. The observed beating signal oscillates at an atomic transition frequency, opening the way to novel quantum limited measurements of atomic resonance frequencies and quantum switches.

We consider a narrow magneto-dipole transition in the Tm-169 atom at the wavelength of 1.14 mu m as a candidate for a two-dimensional-optical lattice clock. Calculating dynamic polarizabilities of the two clock levels [Xe]4f(13)6s(2)(J = 7/2) and [Xe]4f(13)6s(2)(J = 5/2) in the spectral range from 250 to 1200 nm, we find a "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 x 10(-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 x 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 [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.

To study the possible variation of the fine structure constant, α, in laboratory experiments, we propose using narrow lines that correspond to atomic transitions between close lying, long-lived atomic states of different configurations. The small transition frequency, coupled with differences in the electron structure ensures a strong enhancement of the relative frequency change compared to a possible change in α. The small linewidth makes it possible to perform very accurate measurements. These two features, when combined, make the measurements very sensitive to any variation of α.

Pattern formation near threshold in large-aspect-ratio, single-longitudinal-mode, two-level lasers with plane mirrors under the action of a weak injected plane-wave field resonant with the atomic transition frequency and tilted with respect to the laser cavity axis is analytically investigated in terms of the amplitude equations for the system. It is shown that, when the laser emission occurs off-axis, the appearance of resonances among the injected signal field and the unstable emerging tilted waves drastically changes the pattern selection properties of the free-running laser. As a result new transverse patterns, which include singly and doubly periodic stripes and undulating hexagons, may be stabilized by the injected signal. These patterns arise from the superposition of the forced mode with either one, two, or three traveling waves on the critical circle of the free-running laser. This is a distinctive feature from similar structures more commonly found in passive optical systems, where complex patterns always arise as a superposition of standing waves. The stability properties of the various patterns and their selection rules are analytically investigated within the amplitude equations.

We report a strictly non-exponential spontaneous decay dynamics of an excited\ntwo-level atom placed inside or at different distances outside a carbon\nnanotube (CN). This is the result of strong non-Markovian memory effects\narising from the rapid variation of the photonic density of states with\nfrequency near the CN. The system exhibits vacuum-field Rabi oscillations, a\nprincipal signature of strong atom-vacuum-field coupling, when the atom is\nclose enough to the nanotube surface and the atomic transition frequency is in\nthe vicinity of the resonance of the photonic density of states. Caused by\ndecreasing the atom-field coupling strength, the non-exponential decay dynamics\ngives place to the exponential one if the atom moves away from the CN surface.\nThus, atom-field coupling and the character of the spontaneous decay dynamics,\nrespectively, may be controlled by changing the distance between the atom and\nCN surface by means of a proper preparation of atomically doped CNs. This opens\nroutes for new challenging nanophotonics applications of atomically doped CN\nsystems as various sources of coherent light emitted by dopant atoms.\n

A single two-level atom in a coherently driven cavity and damped by a broadband squeezed vacuum centered about the atomic transition frequency is studied. A second-order Fokker-Planck equation for this system is obtained without using system size expansion. Effects of detunings and cavity decays are also incorporated in the Fokker-Planck equation. This equation is used to study atomic inversion, fluorescent spectrum, and the intensity correlations of the transmitted and fluorescent photons in the bad-cavity limit. Several interesting effects in the atomic inversion, spectrum, and intensity correlations due to the squeezed vacuum are presented. These results are also compared with an atom that is damped by a thermal reservoir.