Optical Molasses Research Articles

Bose-Einstein Condensation by Polarization Gradient Laser Cooling.

Attempts to create quantum degenerate gases without evaporative cooling have been pursued since the early days of laser cooling, with the consensus that polarization gradient cooling (PGC, also known as "optical molasses") alone cannot reach condensation. In the present work, we report that simple PGC can generate a small Bose-Einstein condensate (BEC) inside a corrugated micrometer-sized optical dipole trap. The experimental parameters enabling BEC creation were found by machine learning, which increased the atom number by a factor of 5 and decreased the temperature by a factor of 2.5, corresponding to almost 2 orders of magnitude gain in phase space density. When the trapping light is slightly misaligned through a microscopic objective lens, a BEC of ∼250 ^{87}Rb atoms is formed inside a local dimple within 40ms of PGC after MOT loading.

Measurements and analysis of response function of cold atoms in optical molasses

We report our experimental measurements and theoretical analysis of the position response function of cold atoms in a magneto-optical trap (MOT) by applying a transient homogeneous magnetic field as a perturbing force. We observe a transition from a damped oscillatory motion to an over-damped relaxation, stemming from a competition between the viscous drag provided by the optical molasses and the restoring force of the MOT. Our observations are in agreement with the predictions of our model based on the Langevin equation. We also study the diffusion of the atomic cloud in the optical molasses and find the measured value of diffusion coefficient matching with the prediction of our theoretical model.

PyLCP: A Python package for computing laser cooling physics

We present a Python object-oriented computer program for simulating various aspects of laser cooling physics. Our software is designed to be both easy to use and adaptable, allowing the user to specify the level structure, magnetic field profile, or the laser beams' geometry, detuning, and intensity. The program contains three levels of approximation for the motion of the atom, applicable in different regimes offering cross checks for calculations and computational efficiency depending on the physical situation. We test the software by reproducing well-known phenomena, such as damped Rabi flopping, electromagnetically induced transparency, stimulated Raman adiabatic passage, and optical molasses. We also use our software package to quantitatively simulate recoil-limited magneto-optical traps, like those formed on the narrow 1S→30P1 transition in 88Sr and 87Sr.

Fingerprints of nonequilibrium stationary distributions in dispersion relations

Distributions different from those predicted by equilibrium statistical mechanics are commonplace in a number of physical situations, such as plasmas and self-gravitating systems. The best strategy for probing these distributions and unavailing their origins consists in combining theoretical knowledge with experiments, involving both direct and indirect measurements, as those associated with dispersion relations. This paper addresses, in a quite general context, the signature of nonequilibrium distributions in dispersion relations. We consider the very general scenario of distributions corresponding to a superposition of equilibrium distributions, that are well-suited for systems exhibiting only local equilibrium, and discuss the general context of systems obeying the combination of the Schrödinger and Poisson equations, while allowing the Planck’s constant to smoothly go to zero, yielding the classical kinetic regime. Examples of media where this approach is applicable are plasmas, gravitational systems, and optical molasses. We analyse in more depth the case of classical dispersion relations for a pair plasma. We also discuss a possible experimental setup, based on spectroscopic methods, to directly observe these classes of distributions.

Long-range density patterns in a six-beam optical lattice from polarization interference

We report a correlation between periodic patterns of cold-atom density and field polarization that gives new insight into a nearly 30 year old question about the role of optical phases in laser cooling. The laser field of three intersecting pairs of counter-propagating σ + − σ − beams is widely used for cooling of atoms in magneto-optical traps and optical molasses. This six-beam optical lattice differs from four-beam lattices in having two “excess” phase constants of the optical standing waves. These relative time phases are independent degrees of freedom that affect key lattice properties, such as the polarization of the potential wells and the sub-Doppler cooling process. In this work, we create one-dimensional and two-dimensional spatial gradients of the optical phases in a six-beam lattice by slightly tilting the retro-reflected beams. This tilt imparts a long-range periodicity ( ∼ m m ) to the lattice polarization, creating a superlattice in which atoms are seen to diffuse into a periodic density distribution over several milliseconds. We find that high density is correlated with low field ellipticity; atoms move preferentially into regions where the field is linearly polarized. Such a non-uniform density may be important in cold collision experiments and may have applications in the preparation of atoms for atomic clocks and quantum computation.

Manipulating cold atoms through a high-resolution compact system based on a multimode fiber.

We show that a standard multimode optical fiber can act as a high-resolution ultra-compact tool to manipulate cold atoms in setups with limited optical access. Spatial light modulators allow us to generate control beams at the in-vacuum fiber end by digital optical phase conjugation. With no additional in-vacuum optics, this system reaches a $ \sim 1\;{\unicode{x00B5}{\rm m}} $∼1µm resolution for a transverse size of only 225 µm. As a demonstration, we use it to optically transport cold atoms towards the in-vacuum fiber end, to load them in optical microtraps, and to re-cool them in optical molasses. This work shows that the rapid progress of optics in complex media opens new, to the best of our knowledge, perspectives for spatially constrained quantum technology platforms combining cold atoms with other optical, electronic, or opto-mechanical systems.

Cold-atom clock based on a diffractive optic.

Clocks based on cold atoms offer unbeatable accuracy and long-term stability, but their use in portable quantum technologies is hampered by a large physical footprint. Here, we use the compact optical layout of a grating magneto-optical trap (gMOT) for a precise frequency reference. The gMOT collects 107 87Rb atoms, which are subsequently cooled to 20 µK in optical molasses. We optically probe the microwave atomic ground-state splitting using lin⊥lin polarised coherent population trapping and a Raman-Ramsey sequence. With ballistic drop distances of only 0.5 mm, the measured short-term fractional frequency stability is 2×10-11/τ.

Asymmetric heat transport in ion crystals.

We numerically demonstrate heat rectification for linear chains of ions in trap lattices with graded trapping frequencies, in contact with thermal baths implemented by optical molasses. To calculate the local temperatures and heat currents we find the stationary state by solving a system of algebraic equations. This approach is much faster than the usual method that integrates the dynamical equations of the system and averages over noise realizations.

Laser cooling and magneto-optical trapping of molecules analyzed using optical Bloch equations and the Fokker-Planck-Kramers equation

We study theoretically the behavior of laser-cooled calcium monofluoride (CaF) molecules in an optical molasses and magneto-optical trap (MOT), and compare our results to recent experiments. We use multi-level optical Bloch equations to estimate the force and the diffusion constant, followed by a Fokker-Planck-Kramers equation to calculate the time-evolution of the velocity distribution. The calculations are done in three-dimensions, and we include all the relevant energy levels of the molecule and all the relevant frequency components of the light. Similar to simpler model systems, the velocity-dependent force curve exhibits Doppler and polarization-gradient forces of opposite signs. We show that the temperature of the MOT is governed mainly by the balance of these two forces. Our calculated MOT temperatures and photon scattering rates are in broad agreement with those measured experimentally over a wide range of parameters. In a blue-detuned molasses, the temperature is determined by the balance of polarization gradient cooling, and heating due to momentum diffusion, with no significant contribution from Doppler heating. In the molasses, we calculate a damping rate similar to the measured one, and steady-state temperatures that have the same dependence on laser intensity and applied magnetic field as measured experimentally, but are consistently a few times smaller than measured. We attribute the higher temperatures in the experiments to fluctuations of the dipole force which are not captured by our model. We show that the photon scattering rate is strongly influenced by the presence of dark states in the system, but that the scattering rate does not go to zero even for stationary molecules because of the transient nature of the dark states.

Direct Magneto-Optical Compression of an Effusive Atomic Beam for Application in a High-Resolution Focused Ion Beam

An atomic rubidium beam formed in a 70 mm long two-dimensional magneto-optical trap (2D MOT), directly loaded from a collimated Knudsen source, is analyzed using laser-induced fluorescence. The longitudinal velocity distribution, the transverse temperature and the flux of the atomic beam are reported. The equivalent transverse reduced brightness of an ion beam with similar properties as the atomic beam is calculated because the beam is developed to be photoionized and applied in a focused ion beam. In a single two-dimensional magneto-optical trapping step an equivalent transverse reduced brightness of $(1.0\substack{+0.8-0.4})$ $\times 10^6$ A/(m$^2$ sr eV) was achieved with a beam flux equivalent to $(0.6\substack{+0.3-0.2})$ nA. The temperature of the beam is further reduced with an optical molasses after the 2D MOT. This increased the equivalent brightness to $(6\substack{+5-2})$$\times 10^6$ A/(m$^2$ sr eV). For currents below 10 pA, for which disorder-induced heating can be suppressed, this number is also a good estimate of the ion beam brightness that can be expected. Such an ion beam brightness would be a six times improvement over the liquid metal ion source and could improve the resolution in focused ion beam nanofabrication.

New approaches in deep laser cooling of magnesium atoms for quantum metrology

Two approaches for solving the long-standing problem of deep laser cooling of neutral magnesium atoms are proposed. The first one uses optical molasses with orthogonal linear polarizations of light waves. The second approach involves a ‘nonstandard’ magneto-optical trap (NMOT) composed of light waves with elliptical polarizations (in general). Both the widely used semiclassical approach based on the Fokker–Planck equation and quantum treatment fully taking into account the recoil effect are employed for theoretical analysis. The results show the possibility of obtaining temperatures lower than 100 µK simultaneously with a large number of cold atoms ~106 ÷ 107. A new velocity-selective cooling technique allowing one to reach the microkelvin temperature range is also proposed. This technique may have some advantages over, for instance, the shallow-dipole-trap technique utilized by other authors. In the case of magnesium atoms this new technique may be used for obtaining a large number of ultracold atoms (T ~ 1 µK, N > 105). Such a large number of ultracold atoms is crucial issue for metrological and many other applications of cold atoms.

Generation of a cold pulsed beam of Rb atoms by transfer from a 3D magneto-optic trap

We demonstrate a technique for producing a cold pulsed beam of atoms by transferring a cloud of atoms trapped in a three dimensional magneto-optic trap (MOT). The MOT is loaded by heating a getter source of Rb atoms. We show that it is advantageous to transfer with two beams (with a small angle between them) compared to a single beam, because the atoms stop interacting with the beams in the two-beam technique, which results in a Gaussian velocity distribution. The atoms are further cooled in optical molasses by turning off the MOT magnetic field before the transfer beams are turned on.

Production and characterization of a dual species magneto-optical trap of cesium and ytterbium.

We describe an apparatus designed to trap and cool a Yb and Cs mixture. The apparatus consists of a dual species effusive oven source, dual species Zeeman slower, magneto-optical traps in a single ultra-high vacuum science chamber, and the associated laser systems. The dual species Zeeman slower is used to load sequentially the two species into their respective traps. Its design is flexible and may be adapted for other experiments with different mixtures of atomic species. The apparatus provides excellent optical access and can apply large magnetic bias fields to the trapped atoms. The apparatus regularly produces 10(8) Cs atoms at 13.3 μK in an optical molasses, and 10(9) (174)Y b atoms cooled to 22 μK in a narrowband magneto-optical trap.

How cold atoms got hot: an interview with William Phillips

Abstract William Phillips of the National Institute of Standards and Technology (NIST) in Gaithersburg, Maryland, shared the 1997 Nobel Prize in physics for his work in developing laser methods for cooling and trapping atoms. Interactions between the light field and the atoms create what is dubbed an ‘optical molasses’ that slows the atoms down, thereby reducing their temperature to within a fraction of a degree of absolute zero. These techniques allow atoms to be studied with great precision, for example measuring their resonant frequencies for light absorption very accurately, so that these frequencies may supply very stable timing standards for atomic clocks. Besides applications in metrology, such cooling methods can also be used to study new fundamental physics. The 1997 Nobel award was widely considered to be a response to the first observation in 1995 of pure Bose–Einstein condensation (BEC), in which a collection of bosonic atoms all occupy a single quantum state. This quantum-mechanical effect only becomes possible at very low temperatures, and the team that achieved it, working at JILA operated jointly by the University of Colorado and NIST, used the techniques devised by Phillips and others. Since then, cold-atom physics has branched in many directions, among them being attempts to make a quantum computer (which would use logic operations based on quantum rules) from ultracold trapped atoms and ions. ‘National Science Review’ spoke with Phillips about the development and future potential of the field.

NIM5 Cs fountain clock and its evaluation

The cesium fountain primary frequency standard NIM5 has been developed at the National Institute of Metrology in China. The NIM5 loads atoms in an optical molasses from the background Cs vapor directly. Atoms are then cooled to a temperature of about 2 μK and launched to a height of 81 cm. The fringes of the Ramsey pattern have a width of 0.98 Hz. The NIM5 operates for more than 300 d a year, operating nearly continuously for 15 d at a time. By stabilizing the 9.19 GHz microwave frequency to the center of the central Ramsey fringe, a typical fractional frequency instability of 3 × 10−13 (τ/s)−1/2 is obtained when running at high atom density, and a combined uncertainty, including Type A and B uncertainties, is typically 1.6 × 10−15. Comparisons of data between NIM5 and 5 other fountain clocks were carried out in May 2013 via two-way satellite time and frequency transfer (TWSTFT), and the results show good agreement within the uncertainties. Six groups of NIM5 data from January to June 2014 have been published in Circular T 319 and 320.

Optical collimation of an atomic beam using a white light molasses

We investigate optical collimation of an atomic beam using a spectrally broadened white light molasses. We compare this technique with the standard technique using an atomic collimator and find that, under certain conditions, the white light molasses is preferable. Specifically, a white light molasses is suitable for atomic beams with relatively low mean velocities and broad velocity distributions, for example, a beam effusing from a cryogenically cooled reservoir. This result is demonstrated by numerically modeling the atomic trajectories of argon atoms effusing from a cryogenically cooled reservoir. We find that, given sufficient power, a white light molasses captures a larger fraction of atoms when compared to an atomic collimator, and the velocity distribution of the resulting beam is shifted toward slower velocities. Further, an optical molasses is geometrically relatively simple compared to an atomic collimator; therefore, the complexity of the in-vacuum optical arrangement can be significantly reduced.

Phase-space properties of magneto-optical traps utilising micro-fabricated gratings.

We have used diffraction gratings to simplify the fabrication, and dramatically increase the atomic collection efficiency, of magneto-optical traps using micro-fabricated optics. The atom number enhancement was mainly due to the increased beam capture volume, afforded by the large area (4cm(2)) shallow etch (~ 200nm) binary grating chips. Here we provide a detailed theoretical and experimental investigation of the on-chip magneto-optical trap temperature and density in four different chip geometries using (87)Rb, whilst studying effects due to MOT radiation pressure imbalance. With optimal initial MOTs on two of the chips we obtain both large atom number (2×10(7)) and sub-Doppler temperatures (50 μK) after optical molasses.

Temperature and phase-space density of a cold atom cloud in a quadrupole magnetic trap

We present studies on the modifications in temperature, number density and phase-space density when a laser cooled atom cloud from the optical molasses is trapped in a quadrupole magnetic trap. Theoretically it is shown that for a given temperature and size of the cloud from the molasses, the phase-space density in the magnetic trap first increases with magnetic field gradient and then decreases with it, after attaining a maximum value at an optimum value of magnetic field gradient. The experimentally measured variation in phase-space density in the magnetic trap with the magnetic field gradient has shown the similar trend. However, the experimentally measured values of number density and phase-space density are much lower than their theoretically predicted values. This is attributed to the higher experimentally observed temperature in the magnetic trap than the theoretically predicted temperature. Nevertheless, these studies can be useful to set a higher phase-space density in the trap by setting the optimum value of field gradient of the quadrupole magnetic trap.

Sisyphus cooling of lithium

Laser cooling to sub-Doppler temperatures by optical molasses is thought to be inhibited in atoms with unresolved, near-degenerate hyperfine structure in the excited state. We demonstrate that such cooling is possible in one to three dimensions, not only near the standard D2 line for laser cooling, but over a range extending to the D1 line. Via a combination of Sisyphus cooling followed by adiabatic expansion, we reach temperatures as low as 40 \mu K, which corresponds to atomic velocities a factor of 2.6 above the limit imposed by a single photon recoil. Our method requires modest laser power at a frequency within reach of standard frequency locking methods. It is largely insensitive to laser power, polarization and detuning, magnetic fields, and initial hyperfine populations. Our results suggest that optical molasses should be possible with all alkali species.

High-Sensitivity In situ Fluorescence Imaging of Ytterbium Atoms in a Two-Dimensional Optical Lattice with Dual Optical Molasses

We developed a dual molasses technique which enabled us to perform high-sensitivity in situ fluorescence imaging of ytterbium (Yb) atoms in a two-dimensional optical lattice prepared in a thin glass cell. This technique successfully combines two different kinds of optical molasses for Yb atoms, that is, the one using the 1S0–1P1 transition which provides high-resolution in the in situ fluorescence imaging and the other using the 1S0–3P1 transition for cooling the atoms in the optical lattice. We performed in situ imaging of 174Yb atoms and could observe a Moiré pattern with a period of about 6 µm produced by the molasses beam with 556 nm and the optical lattice with 532 nm, which implies that the temperature was kept below the lattice depth during the fluorescence imaging. The number of photons per atom is estimated to be enough for single atom detection with our imaging system. This result is quite promising for the realization of an Yb quantum gas microscope.