• Quantum Logic Gates. The ability to coherently manipulate quantum systems should lead to dramatic breakthroughs in quantum information processing, quantum communication, and precision measurements. The Quantum Processes Group has therefore carried out theoretical simulations to show how collisions of trapped neutral atoms in optical lattice cells may be used to create entanglement between the atoms, thereby allowing high fidelity quantum logic gate operations.

Our work has characterized the robustness and speed of the entanglement process when motional states of atoms in a two-color optical lattice form the qubits and the atom-atom interaction is turned on and off by controling the two laser intensities. When the barrier separating the individual optical wells is lowered by changing the relative intensity of the two lasers, the atoms tunnel through the barrier and the atom-atom interaction entangles the qubits. Figure 3 illustrates an example of a two-atom wavefunction for the two cases when the barrier is either high or low. We have shown that by properly controlling the time-dependent laser intensities a controlled quantum interference can be used to reduce the decoherence of the entanglement process to below 0.001% and simultaneously keep the time to entangle the atoms relatively short. Without the use of the controlled quantum interference a ten times longer entangling time is needed for the same decoherence rate. Moreover, we have demonstrated that the idea of using a controlled interference is not limited to entangling operations of qubits based on neutral atoms. It should be useful for other qubit implementations as well. (E. Tiesinga, C.J. Williams, F. Mies, E. Charron)

Figure 3. Contour plot of a wavefunction for two interacting atoms in a one-dimensional double well potential with a barrier between the two wells. A high barrier localizes one atom in each well, whereas a low barrier allows both atoms to occupy the same well.

• Quantum Dot Clusters. The analogy of quantum dots (QD) and nanocrystals as artificial atoms is now well established and has driven diverse applications from integrated laser devices to biosensors and biomarkers to quantum computing. We have explored the next step, the development of nanocircuits of quantum dot nanodevices, by simulating the properties of clusters of QDs (artificial molecules and nanoarchitectures) and arrays of QDs (quantum dot solids).

  We developed previously an atomistic tight-binding simulator for the electronic and optical properties of individual QDs and nanocrystals. This past year we have extended these simulations to consider artificial molecules, quantum dot solids and nanoarchitectures. The first step was to understand simple coupled QDs, as shown in fig. 4 for two core/shell CdS/ZnS nanocrystals, and to establish the bounds for the analogy between coupled dots and artificial molecules. Coupled core/shell nanocrystals and stacked pyramidal dots grown by self-organized molecular beam epitaxy have been simulated. In each case, we have found that the conduction states in the coupled nanostructures closely follow the analogy with molecular states. Hybridized conduction states form σ and π interdot bonds. State energies and polarization depend on this bonding. Valence-state interdot-hybridization produces significant level reordering and drastic changes in oscillator strengths. Hybridization of valence states is complex and cannot be described just in analogy with molecular hybridization. (G.W. Bryant, W. Jaskolski)

Figure 4. Schematic diagram of two interacting quantum dots with an inner core of ZnS and an outer layer of CdS. A typical dot diameter is on the order of 5 nm.

• Cold Cesium Mysteries Solved. Researchers in the Quantum Processes Group have solved a long-standing problem by constructing a quantitative model of collisions of ultracold cesium atoms. Atomic cesium is an important species that has been the object of numerous cooling and trapping experiments. Laser cooled cesium is also the basis of the new NIST F1 cesium atomic fountain clock. In spite of many studies, a quantitative understanding of collisions of cold cesium atoms has proved elusive. It is important to understand these collisions, since collisional shifts in the cesium transition frequency can adversely affect the performance of the fountain clock. In addition, the collisional properties of cesium atoms have prevented the achievement of Bose-Einstein condensation in cold cesium atomic gases.

  Collisions of very cold atoms are different from normal high temperature collisions in that they are strongly affected by special quantum effects associated with the very long De Broglie wavelength of the colliding atoms. However, a collision model with only four key parameters characterizes the full quantum dynamics of cold cesium collisions. Two of these parameters are known as scattering lengths, which determine clock shifts and the stability of a Bose-Einstein condensate. One is the coefficient that gives the magnitude of the long-range force between the two atoms. The other expresses the effective interaction between the two electron spins as modified by chemical bonding effects in the cesium dimer molecule. This latter parameter strongly affects the collisional losses that hinder Bose-Einstein condensation.

The NIST group set out to explain all previously existing data on cold cesium collisions. A key to the analysis were new data provided by experiments in the group of Stephen Chu at Stanford University, which used a magnetic field to tune a number of cesium dimer bound states to be in resonance with the colliding atoms. Fitting to the Stanford data determined the four parameters. The resulting quantitative model not only accounts for all known data on ground state cold cesium atom collisions but also accurately predicted locations for a number of resonances prior to measurement. Figure 5 compares our model calculations (dashed) with typical Stanford data (solid) on collision rate versus magnetic field. The new model, contrary to previous expectations, predicts that the collisional shift in a cesium fountain clock could be greatly reduced if the clock could be operated at a much lower temperature in the range of 50 nanokelvin. The model also makes specific predictions for what range of magnetic fields Bose-Einstein condensation of cesium might be possible. (C.J. Williams, P.S. Julienne, and P. Leo)

Figure 5. Inelastic collision rate constant versus magnetic field (in mT) for two cold, trapped Cs atoms in a particular ground state Zeeman sublevel.

• Nano-optics. Nano-optics is a rapidly emerging branch of optics driven by the need to control and manipulate light on the nanoscale for use in, for example, photonic devices and circuits, microscopy with nanometer resolution, and atom trapping and guiding. To fully understand the physics issues, we have simulated light fields on the nanoscale with applications to near-field scanning optical microscopy (NSOM), quantum computing and single molecule spectroscopy.

  NSOM has been used intensively at NIST to obtain nanoscale resolution in optical microscopy. The key to NSOM is to place a nanoscale optical probe in the near-field of the sample. A critical challenge for NSOM metrology is to identify and quantify the mechanisms that provide contrast in NSOM images. Even the simplest samples can provide counterintuitive images that are difficult to interpret. Holes in a dielectric film appear dark in NSOM images despite the expectation that probe light would pass most easily through the holes. We have therefore simulated this case and could show that the image contrast is determined by how light is extracted from the NSOM probe rather than how the probe light propagates through the hole. The holes are dark in NSOM images because less light is extracted from the probe when the probe is above a hole. This simple but surprising explanation provides another step toward making NSOM a qualitatively and quantitatively accurate nanoscale metrology. (G.W. Bryant, A. Rahmani)

• EBIT Tests Remote Temperature Diagnostic. In order to assist NASA scientists in measuring the temperature of hot plasmas, a team of scientists from NIST, the Harvard-Smithsonian Center for Astrophysics, the Naval Research Laboratory, the Observatory of Palermo (Italy), NASA Goddard Space Flight Center, MIT, and the Lawrence Berkeley National Laboratory have worked together on an experiment that took place at the NIST EBIT facility. Precisely controlled x-ray spectra from highly ionized iron and krypton atoms (16 and 26 electrons/atom removed, respectively) were produced by using an intense, monoenergetic electron beam threaded through a cryogenic ion trap. The highly ionized atoms were held at a temperature of approximately 5 million Kelvin while x-rays were measured with a prototype microcalorimeter detector of the sort being developed for future space missions. Spectra were collected with better than 6 eV resolution using a single detector that covered the broad spectral range from 10,000 eV to 500 eV. By simultaneously observing resonance lines and radiative recombination from the monoenergetic electron beam, it was possible to determine cross sections for electron impact excitation of the individual resonance lines. In field observations, the temperature is inferred from the ratio of spectral line strengths, assuming that the underlying atomic physics is calculable. But the benchmark spectra and cross sections obtained from the experiment at the NIST facility indicate that a key astrophysical temperature diagnostic is not valid. The experiment has thus stimulated work at other institutions to develop an improved diagnostic. (E. Takacs, I. Kink, and J.D. Gillaspy)

• Sub-millimeter Wave Spectroscopy of Etching Plasmas. Sub-millimeter wave absorption spectroscopy has been applied to etching type plasmas for the identification and monitoring of plasma species. As semiconductor wafer-size grows and feature-size shrinks, monitoring and control of the basic plasma chemistry has become increasingly important for ensuring fidelity and performance of microelectronic devices. Sub-mm wave spectroscopy can monitor the crucial chemical species and provide the necessary feedback for understanding plasma processing. Our measurements have concentrated on the use of a backward wave oscillator (BWO) as the sub-mm wave source since this device is relatively compact and could easily be utilized in an industrial setting. We have identified chemical species found in fluorocarbon etching-type plasmas created in the inductively coupled version of the GEC RF Reference Cell. The GEC Cell creates plasmas similar to those used in commercial etching reactors, but has numerous ports for diagnostic access. Spectra from 10 molecules have been identified including feed gases (CHF₃, CF₃I), etching radicals (CF₂, CF), etching byproducts (CO, COF₂, SiO, SiF₂, SiF) and contaminants (H₂O). The diagnostic has been used to measure the dissociation of CHF₃ and the relative dependence of various species on plasma conditions. Spectral resolution of the BWO is so high that it could also be used to measure the translational gas through the Doppler broadening of the absorption line shapes. These gas temperatures are important input parameters to many plasma models since they are necessary to relate the measured gas pressure to the actual particle density in the chamber. The gas temperatures measured of several different plasma species have all been at or only slightly above room temperature (see fig. 6). (E. Benck with G. Golubyatnikov and G. Fraser, Div. 844)

Figure 6. Second harmonic frequency modulated absorption signal of CF in a CF4 inductively coupled discharge. The smooth curve is a line shape model fitted to the data corresponding to a gas temperature of 346 °K.

UV Intrinsic Birefringence of CaF2 and BaF2. We made the first measurements of an intrinsic birefringence in the UV materials CaF2 and BaF2, which are the primary optical materials considered for 157 nm optical lithography, to be used for future-generation integrated circuit fabrication. The measured birefringences are more than ten times the design tolerances for residual birefringence for 157 nm lithography systems, and all such designs will now have to be substantially modified to account for this effect. This result was unanticipated by the industry because it was assumed that the cubic symmetry of these crystals would insure isotropy of the optical properties, which in fact is only true for long wavelengths. As can be seen in the plot of our measurements below, the relatively large magnitudes of the intrinsic birefringences near 157 nm decrease rapidly to unmeasureable values in the visible, explaining why previous residual birefringence measurements of these materials in the visible did not reveal the effect. Our measurements were done in conjunction with theoretical analyses and calculations by Z. Levine (Electron Optical Physics Division) and E. Shirley (Optical Technology Division), shown by the curves in fig. 7. We first showed how the symmetry of this effect can be exploited for compensation by coupling lenses with differing crystal axis orientations. We also showed that due to the opposite sign of the effect for CaF2 and BaF2, it can in principale be eliminated entirely by creating appropriate mixed crystals Ca1-xBaxF2. All 157 nm systems are now being designed using at least one of these correction approaches. (J.H. Burnett)

Figure 7. Measurements (symbols) and calculations (curves) of intrinsic birefringence of CaF2 and BaF2 as functions of wavelength (with standard uncertainties).

• Ultracold Collisions. Starting with one laser to photoassociate slowly colliding atoms into bound states of excited diatomic molecules in a magneto-optical trap, we then used additional lasers to take these molecules into either doubly-excited states or to bound ground-state molecules. New spectroscopy of the uppermost bound states of the triplet ground state of Na₂ has been obtained. In addition, the production of stable ground-state molecules in a number of these states has been demonstrated and the detection of the molecules, in a state-selective manner, has been demonstrated as well. Pulsed-laser, pump-probe photoassociation experiments were carried out that show indications of the dynamics of the photoassociation-ionization process. Pairs of atoms are excited to singly-excited states with a first (pump) pulse and then to doubly-excited states that autoionize with a second (probe) pulse. In order to autoionize they must survive on the doubly-excited potential into small internuclear separations. These experiments have demonstrated the importance of the travel on the strongly attractive singly-excited molecular potentials in the dynamics of the process. Population excited to these levels at long range is able to accelerate toward smaller separations, increasing their chance of survival against spontaneous emission and also bypassing the angular momentum barriers that exist on the relatively flat ground-state and doubly-excited-state potentials. (L. deAraujo, S. Gensemer, K. Jones, and P. Lett)

• Ultracold Plasmas. In an ultracold plasma produced by photoionization of a laser-cooled gas of metastable xenon we had previously measured that, at the coldest and densest parameters we could achieve, the plasma expanded with seemingly more energy than had been put in by the laser photons. In a search for a reservoir of negative (i.e., binding) energy in the form of atoms (which would assure energy conservation) we undertook an experiment that used selective field ionization to measure the formation of Rydberg atoms. We found that a substantial fraction (up to 30%) of the plasma recombines into these neutral Rydberg atoms. Summing up the binding energy in the Rydbergs did seem to account for the excess expansion energy, but these atoms were formed over a much longer time period than that of the appearance of the expansion energy. In fact, significant Rydberg formation occurred even after the plasma density dropped by 4 orders of magnitude. Based on our findings, the exact mechanism of the recombination is currently under investigation by several theoretical groups. The leading explanation is a "freezing out" of electron-ion correlations present in the plasma as it expands. We have undertaken collaborations with theoretical groups at Los Alamos National Lab and Auburn Univ. to address this problem. (M. Lim, J. Roberts, S. Rolston)

• Optical Tweezers. We have observed real-time adhesion between a monoclonal antibody and its specific antigen in an experiment using optical tweezers. Both antibody and antigen molecules are immobilized on the surfaces of (different) polystyrene microspheres, which are trapped by separate optical tweezers. The monitoring of spontaneous, thermally driven, successive attachment and detachment events has allowed a direct determination of the reaction-limited detachment rate for a single bond and also for multiple bonds. A second experimental direction has been studying the use of liposomes as bioreactors. For this purpose we have set up a new experiment employing two optical-tweezer traps and an optical scalpel (a UV laser that can pierce the wall of a liposome). With this new apparatus, we are able to trap two liposomes and fuse them together, thus allowing their contents to mix. In a first experiment, we demonstrated the fusion of a dye-encapsulated liposome with another liposome and observed, with fluorescence microscopy, the mixing of the dye. (K. Helmerson, R. Kishore, and S. Kulin)

• Quantum Computing in Optical Lattices. We have achieved Bose-Einstein condensation (BEC) in rubidium vapor. A new apparatus was constructed in which rubidium atoms were loaded from a Zeeman-tuned, slowed atomic beam into a magneto-optical trap (MOT) and then transferred into a magnetic trap. The atoms were then evaporatively cooled and condensed into the lowest energy state in the trap. This source of atoms will be used to load 1-D and 3-D optical lattices for investigation of different quantum logic gate designs for neutral atom quantum computing. (B. King, S. Peil, T. Porto, and S. Rolston)

• Optical Interactions in Bose-Einstein Condensates. An experiment to observe "dynamical tunneling" was performed in collaboration with researchers from the University of Queensland, Australia. For a wheel spinning clockwise or counter-clockwise there is energetically no difference between the two motions, and classically to reverse the sense of rotation requires the wheel to stop. But quantum mechanics allows the system to "tunnel" from one state to another even if it is classically forbidden. Tunneling has been observed since the early days of quantum mechanics, but usually involves traversing a barrier that, classically, a particle does not have enough energy to go over. Dynamical tunneling, predicted in the early 80s, is similar, but some constant of the motion other than energy classically forbids the quantum mechanically-allowed motion. We observed classically forbidden motion of atoms transferring between two modes of oscillation in the potential wells formed by an amplitude-modulated optical standing-wave. Atoms were loaded from a BEC into the bottom of the optical potentials, and were induced to oscillate back and forth by a sudden displacement of the standing wave. The number of atoms in this particular oscillatory motion was observed to decrease with time, as a group of atoms began to appear oscillating 180^o out of phase with the initial motion. Eventually, almost all of the atoms ended up in the out-of-phase motion, but then tunneled back to the initial mode of oscillation (see fig. 8). We observed up to eight coherent transfers of atoms back and forth between the two stable motions due to dynamical tunneling. No atoms were observed to exhibit motion intermediate between the two stable oscillatory motions (for example, corresponding to atoms stopping and reversing direction), providing further confirmation that the transfer of atoms was due to dynamical tunneling. (A. Browaeys, H. Haeffner, K. Helmerson, W. Hensinger, C. McKenzie, W. Phillips, S. Rolston, and B. Upcroft)

Figure 8. Dynamical tunneling in the quantum driven pendulum. The figure shows the momentum distribution of atoms released from an amplitude-modulated potential for three different times after a BEC was loaded into the potential (0.25, 2.25, and 5.25 modulation periods (f=250 kHz)). The classical result from this system would have the momentum distribution remain stationary in this stroboscopic picture. It is evident that the state of motion of the atoms is in fact oscillating back and forth, a signature of coherent dynamical tunneling. The individual peaks are separated in momentum by 2 ħk which corresponds to a velocity of 6 cm/s for sodium.

• BEC in 1-D Lattices. We have performed a series of experiments with a BEC in a 1-D optical lattice. Making use of the small momentum spread of a BEC and of atom optics techniques, a high level of coherent control over an artificial solid-state-like system was demonstrated. We were able to efficiently load the BEC into the lowest lattice band (and other bands) with different quasi-momentum q by varying the lattice amplitude and lattice velocity relative to the BEC. By adiabatically increasing the lattice amplitude, more than 99% of the BEC could be loaded into the lattice ground state. Such experiments are needed to evaluate the possibility of using neutral atoms in off-resonant optical lattice potentials for quantum information processing.

  Using either phase or amplitude modulation of the optical lattice, we have coherently transferred population between various lattice band states. For example, we have used amplitude modulation to transfer atoms from the ground band to the second excited band for various initial q, allowing a direct measurement of the curvature of the second excited band.

  We have also demonstrated a large-momentum atom beam splitter based on coherent Bragg diffraction followed by acceleration of the BEC in an accelerating optical lattice. Bragg diffraction produces atoms in a coherent superposition of 0 and ≈ 2 k, where k is the magnitude of the wavevector of the laser light. The two momentum states could be loaded predominantly into two bands of the lattice (fig. 9). Acceleration of the lattice moved atoms in one band with respect to the other, resulting in a large final momentum (we demonstrated up to 12 k). We have confirmed that the acceleration is coherent by constructing an atom interferometer based on this novel beam splitter. (A. Browaeys, H. Haeffner, K. Helmerson, C. McKenzie, W. Phillips, and S. Rolston)

Figure 9. Time of flight images of the momentum distribution of a BEC that was suddenly loaded into an optical lattice (depth = 14 recoil energies), and held for varying lengths of time (time between each image is 0.5 microseconds). When the BEC is suddenly loaded into a lattice, the wave function is projected into a superposition of various bands. Since each band has a different energy, the relative phases evolve in time. When the lattice is switched off, the populations of the bands are projected onto plane wave states and interferences result in oscillating populations of the various diffraction orders. The top picture (simple oscillations) shows the case where quasi-momentum q= 0 states are populated; the bottom picture depicts the case when q=1 states are populated by switching on a moving lattice.

• Binding Energy Measurements in Light Nuclei. The binding energy of the neutron in several light nuclei has been measured at the Institut Laue Langevin (ILL) using the joint NIST/ILL precision gamma-ray spectrometer that is coupled to the high flux reactor of the ILL. The spectrometer measures the wavelengths of gamma-ray photons using crystals whose lattice spacings are precisely known in SI units and an angle scale that is derived from first principles. Binding energies are obtained by summing the energies (wavelengths) of all γ-rays in a cascade connecting the capture and the ground states. Binding energy measurements are important because (1) they provide high-energy (short wavelength, λ ≈ 0.2 pm) standards and (2) they check the consistency of precision gamma-ray and atomic mass measurements.

  Binding energy measurements have been made in ²⁹Si, ³³S, and ³⁶Cl species chosen because of their large capture cross sections. As an example, the reaction n+³⁵Cl→³⁶Cl+γ's leads to the relation between atomic masses and the neutron binding energy S_n, m(n) + m(³⁵Cl) = m(³⁶Cl) + S_n(³⁶Cl). The binding energies are ≈ 8.6 MeV and the available cascades require the measurement of γ-rays in the 5 MeV to 6 MeV range. In the course of these measurements, we have improved our capability to accurately measure small diffraction angles (< 0.1°) and pioneered the use of thicker crystals and better collimation to improve signal to background at high energies. The relative uncertainty of the binding energy measurements is 2 to 4 parts in 10^-7 which is comparable to the relative uncertainty of the best available atomic mass differences. (E. Kessler with S. Dewey, Div. 846)

• Upgraded Angle Metrology for Absolute Vacuum X-Ray Wavelength Determination. NIST's Vacuum Double Crystal Spectrometer measures absolute x-ray wavelengths from 0.6 Å to 12 Å (1 keV to 20 keV). This is tied to the SI via the lattice spacing of the diffraction crystals. The measurement of absolute wavelengths also requires accurate measurement of the angle at which the diffraction condition is satisfied. This year the crystal angle encoder was upgraded to a device that has smaller errors. Then a new general calibration approach was developed to determine the encoder error function so that even these small errors can be corrected. A twelve-sided optical polygon was used with a nulling autocollimator and the requirement of circle closure (0° = 360°) to first determine the angles between adjacent polygon faces. Then the polygon was phased with respect to the encoder, mapping out its 360° error function twelve points at a time. The fitted error function and its residuals (fit minus measurement) are shown in fig. 10 (a) and (b), respectively.

  Figure 10. (a) The fitted encoder error function and (b) the residuals (fit minus measurement) for the NIST Vacuum Double Crystal X-Ray Spectrometer encoder.

  The magnitude of the error corrections is on the order of 0.5 µrad to 1.0 µrad and the residuals are scattered about zero with a standard error (k=1) of 0.2 µrad (0.00001°). The angle measurement uncertainty contributes < 1 × 10^-6 to the relative uncertainty of the wavelength measurements. This improved calibration scheme will be applied to high precision angle encoders used with other x-ray diffractometers in the Division. (L. Hudson)

• Laser System for Long-range Fabry-Perot Interferometry. Fabry-Perot interferometry provides the highest resolution of any technique for measuring displacements. The standard practice for measuring a displacement consists of locking a tunable laser to a Fabry-Perot cavity resonance, varying the length of the cavity, and monitoring the optical frequency of the laser. This approach has been useful only for measurements of a rather limited range (≈ 1 micrometer). In order to increase the measurement range of Fabry-Perot interferometry, we have built a computer-controlled scanning laser system that probes two adjacent cavity modes. Displacements up to 50 mm can be measured without sacrificing resolution. The system incorporates independent acousto-optic control of the optical frequencies, and employs frequency modulation spectroscopy to provide error signals in a region in which the laser noise is shot-noise limited. The light output was coupled into a single-mode fiber, enabling remote interrogation of a Fabry-Perot cavity in vacuum. The optical frequencies were measured relative to an iodine-stabilized laser, providing a frequency reference with a fractional accuracy of 2.5 × 10^-11. This system complements the progress we have made in heterodyne interferometry and laser stabilization, and should be of particular interest in future experiments involving thermal expansion of materials and x-ray interferometry.

  The attainable resolution is illustrated in fig. 11, where we studied the vibration contributed to a Fabry-Perot interferometer by a turbomolecular vacuum pump at the second harmonic of its rotation frequency. When the pump was on, a peak appeared whose amplitude corresponds to an rms displacement of less than 5 fm, - a size typical of nuclear radii. (J. Lawall, M. Pedulla, and B. Lantz)

Figure 11. Displacement vs frequency plot for our Fabry-Perot system that illustrates the available high resolution.