Ground-state Hyperfine Sublevels Research Articles

Construction and characterization of a continuous atom beam interferometer

In this article, we investigate both theoretically and experimentally the method of Ramsey interference applied to cold atoms being emitted from a 2-dimensional magneto-optical trap (2D-MOT) crossing continuous wave (cw) laser fields that drive Raman transitions between ground-state hyperfine sublevels. In our apparatus, the atomic beam divergence is large (56 mrad half-angle), necessitating the inclusion in our model of both the atomic divergence and the laser beam divergence as well as averaging over the transit time of the atoms through the laser beam. We discuss the effects of the divergence of the atomic and laser beams, and then we describe our apparatus and qualitatively compare our experimental results to the theoretical results. We find good agreement between our model and our experimental results.

Absorption in the 21-cm Line in Primordial Matter Density Fluctuations at the Stage of Their Nonlinear Compression

The mechanisms of absorption formation in the cosmic microwave background (CMB) spectrum at the frequency of the 21-cm line of the transition between the ground-state hyperfine sublevels of the hydrogen atom are analyzed. We show that a strong nonlinearity at the compression stage of primordial matter density fluctuations can give rise to a significant (in depth) absorption even before the explosions of the first stars. In this case, the main effect is due to the heating of matter in a certain narrow range of temperatures under cloud compression. We consider a steady-state radiative transfer in the 21-cm line in a medium that represents a contracting primordial matter density fluctuation at a given redshift z modeled by a homogeneous spherically symmetric cloud in the state of collapse with an adiabatic change in the gas temperature. For a sequence of cloud states with different degrees of compression we have calculated the frequency profiles of the line in the flux of radiation emerging from the cloud. In the initial state we specify the cloud radius r0, while the gas density is assumed to be equal to the mean cosmological density for a given redshift. We show that for a separate cloud at z = 20, r0 = 1 kpc, and a degree of radius compression of 1.9 the absorption depth in the line center can reach 0.9 K. When averaged over an ensemble of clouds, the central frequency of the line and its width are determined by the details of the fluctuation evolution dynamics.

Coherent Raman beat analysis of the hyperfine sublevel coherence properties of 167Er3+ ions doped in an Y2SiO5 crystal

In this paper, we describe the use of coherent Raman beat (CRB) spectroscopy designed to reveal the phase coherence time t2 of the ground state hyperfine sublevels of 167Er3+ ions doped in an Y2SiO5 crystal cooled to a cryogenic temperature. The short optical coherence time T2 (~1μs) and sublevel population lifetime t1 (~0.1s) of the dopant Er3+ ions make it difficult to implement Raman echoes and optically detected spin echoes for measuring t2, respectively. In contrast, CRB is insensitive to the T2 and t1 values and worth employing if we can cope with inhomogeneous dephasing. By comparing carefully with the effects of sublevel inhomogeneous broadening Δ12 on the various Raman signals, we can estimate the t2 value even when t2>1/Δ12. The ground-state t2 values of the Λ-type three-level system identified in the 167Er3+ ions are approximately 12 and 50μs when the dopant concentrations are 0.005 and 0.001at%, respectively. These t2 values are long enough to realize electromagnetically induced transparency and coherent population trapping with an Er3+:Y2SiO5 crystal at a wavelength of 1.5μm.

Study on the relationship between coherent population beating signal and the coherence of ground-state hyperfine sublevels

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.

Polarization of atoms by simultaneous electromagnetic pulses of different frequency ranges

A method is proposed for the fast and deep polarization of a system of ground-state hyperfine sublevels of an atom having an optical excited level or a system of excited-state sublevels. The method is based on the simultaneous action of pulsed bichromatic resonance fields of optical and microwave ranges. The scheme of the ground-state sublevel polarization by bichromatic or monochromatic microwave fields is also considered.

Atomic clocks and coherent population trapping: Experiments for undergraduate laboratories

We demonstrate how to construct and operate a simple and affordable apparatus for producing coherent effects in atomic vapor and for investigating their applications in time-keeping and magnetometry. The apparatus consists of a vertical cavity surface emitting diode laser directly current-modulated using a tunable microwave oscillator to produce multiple optical fields needed for the observation of coherent population trapping. This effect allows very accurate measurement of the transition frequency between two ground state hyperfine sublevels, which can be used to construct a coherent population trapping-based atomic clock.

Nonlinear magneto-optical rotation and Zeeman and hyperfine relaxation of potassium atoms in a paraffin-coated cell

Nonlinear magneto-optical Faraday rotation (NMOR) on the potassium D1 and D2 lines was used to study Zeeman relaxation rates in an antirelaxation paraffin-coated $3\text{\ensuremath{-}}\mathrm{cm}$-diameter potassium vapor cell. Intrinsic Zeeman relaxation rates of ${\ensuremath{\gamma}}^{NMOR}∕2\ensuremath{\pi}=2.0(6)\phantom{\rule{0.3em}{0ex}}\mathrm{Hz}$ were observed. The relatively small hyperfine intervals in potassium lead to significant differences in NMOR in potassium compared to rubidium and cesium. Using laser optical pumping, widths and frequency shifts were also determined for transitions between ground-state hyperfine sublevels of $^{39}\mathrm{K}$ atoms contained in the same paraffin-coated cell. The intrinsic hyperfine relaxation rate of ${\ensuremath{\gamma}}_{\mathit{expt}}^{\mathit{hf}}∕2\ensuremath{\pi}=10.6(7)\phantom{\rule{0.3em}{0ex}}\mathrm{Hz}$ and a shift of $\ensuremath{-}9.1(2)\phantom{\rule{0.3em}{0ex}}\mathrm{Hz}$ were observed. These results show that adiabatic relaxation gives only a small contribution to the overall hyperfine relaxation in the case of potassium, and the relaxation is dominated by other mechanisms similar to those observed in previous studies with rubidium.

Experimental observation of electromagnetically induced transparency in Pr3+:LaF3

We report an experimental observation of electromagnetically induced transparency (EIT) in Pr3+:LaF3 at liquid helium temperature at the 3H4(0)–1D2 (16 872 cm−1) transition. Transparency resonance at ground state hyperfine sublevels (in a Λ scheme) and a dispersion-shaped resonance due to excited state hyperfine coherences (in a V scheme) are detected. Theoretical analysis taking into account the six-level Pr3+ level structure gives qualitative agreement with the experiment.

Quantum Statistical Properties of Photons and Atoms in Interaction of an Atomic Bose–Einstein Condensate with Lasers**The project supported in part by National Natural Science Foundation of China, the Natural Science Foundation of Hunan Province and special project of the NSF Through The Institute of Theoretical Physics, Academia Sinica

In this paper, we study quantum statistical properties of atoms and photons in interaction of -atomic Bose–Einstein condensate in the ground-state hyperfine sublevels with laser fields. We investigate not only quantum conversions between atoms in the condensate and photons in the quantized laser field, but also transfer of nonclassical characteristics of atoms and photons between input states and output states when the atom field is initially in a number state and the quantized laser field is in the even coherent state and the odd coherent state, respectively. We find various conditions to realize these quantum conversions. We also study atom-photon quantum correlations and their input-output conversions. It is indicated that there are atom-field nonclassical correlations.

Proposal for an optical funnel trap

We propose an all-optical method for channelling and cooling a cloud of laser pre-cooled atoms making use of the light-shifts induced by a doughnut-mode laser beam tuned close to the high frequency side of an atomic resonance. We show that inelastic collisions of the atoms with the optical walls of the trap and optical pumping between differently light-shifted ground state hyperfine sublevels induced by a weak auxiliary repumping beam give rise to a cyclical mechanism which results in the simultaneous cooling and channelling of the atoms. Because the heating due to random scattering of photons is offset by this cooling mechanism, our trap does not suffer the lifetime limitation due to heating inherent to previous optical dipole traps. We present, for a variety of parameters, the results of semi-classical Monte Carlo simulations for a three-dimensional model system.

Direct excitation of microwave-spin dressed states using a laser-excited resonance Raman interaction.

We have used a laser-induced resonance Raman transition between the ground-state hyperfine sublevels in a sodium atomic beam to excite individual dressed states of the microwave-spin hyperfine transition. In addition, we have used the microwave interaction to excite the Raman trapped state. Extension of this technique to mm waves or to the far infrared may lead to applications such as mm-wave-beam steering and holographic image conversion.