Adiabatic Sweep Research Articles

Adiabatic passage through a Feshbach resonance in a degenerate quantum gas

The dynamics of an adiabatic sweep through a Feshbach resonance in a degenerate quantum gas of fermionic atoms to produce a degenerate quantum gas of diatomic molecules are studied using many-body and mean-field methods. We demonstrate that the dependence of the remaining fraction of atoms Γ on sweep rate α varies from exponential Landau–Zener behaviour for a single pair of particles, to a power-law dependence for a large number of atoms, N. Two different power-law behaviours are obtained depending on the initial molecular fraction. The two different regimes are described in terms of quantum fluctuations: a linear power-law, Γ∝α, is obtained when the initial molecular fraction is smaller than the 1/N quantum fluctuations, and Γ∝α1/3 when it is larger.

Joint composite-rotation adiabatic-sweep isotope filtration.

Joint composite-rotation adiabatic-sweep isotope filters are derived by combining the composite-rotation [Stuart AC et al. (1999) J Am Chem Soc 121: 5346-5347] and adiabatic-sweep [Zwahlen C et al. (1997) J Am Chem Soc 119:6711-6721; Kupce E, Freeman R (1997) J Magn Reson 127:36-48] approaches. The joint isotope filters have improved broadband filtration performance, even for extreme values of the one-bond (1)H-(13)C scalar coupling constants in proteins and RNA molecules. An average Hamiltonian analysis is used to describe evolution of the heteronuclear scalar coupling interaction during the adiabatic sweeps within the isotope filter sequences. The new isotope filter elements permit improved selective detection of NMR resonance signals originating from (1)H spins attached to an unlabeled natural abundance component of a complex in which the other components are labeled with (13)C and (15)N isotopes.

Sensitivity enhancement of NMR spectra of half-integer spin quadrupolar nuclei in solids using hyperbolic secant pulses

The experimental factors influencing the enhancements achievable for the central NMR transition, m I = 1/2 → m I = −1/2, of spin-3/2 and spin-5/2 nuclei in the solid state using hyperbolic secant, HS, pulses for population transfer are investigated. In the case of powder samples spinning at the magic angle, it is found that the spinning frequency, the bandwidth and the frequency offset of the HS pulse play a crucial role in determining the maximum enhancements. Specifically, the bandwidth must be set to the spinning frequency for maximum signal enhancements. The 87Rb NMR enhancement obtained for RbClO 4 using HS pulses was relatively insensitive to the magic angle spinning frequency; however, in the case of Al(acac) 3, the 27Al enhancement increased with MAS frequency. In order to obtain an adiabatic HS sweep, one should optimize the rf field for a given pulse duration or optimize the pulse duration for a given rf field.

Many-body effects on adiabatic passage through Feshbach resonances

We theoretically study the dynamics of an adiabatic sweep through a Feshbach resonance, thereby converting a degenerate quantum gas of fermionic atoms into a degenerate quantum gas of bosonic dimers. Our analysis relies on a zero temperature mean-field theory which accurately accounts for initial molecular quantum fluctuations, triggering the association process. The structure of the resulting semiclassical phase space is investigated, highlighting the dynamical instability of the system towards association, for sufficiently small detuning from resonance. It is shown that this instability significantly modifies the finite-rate efficiency of the sweep, transforming the single-pair exponential Landau-Zener behavior of the remnant fraction of atoms Gamma on sweep rate alpha, into a power-law dependence as the number of atoms increases. The obtained nonadiabaticity is determined from the interplay of characteristic time scales for the motion of adiabatic eigenstates and for fast periodic motion around them. Critical slowing-down of these precessions near the instability leads to the power-law dependence. A linear power law $Gamma\propto alpha$ is obtained when the initial molecular fraction is smaller than the 1/N quantum fluctuations, and a cubic-root power law $Gamma\propto alpha^{1/3}$ is attained when it is larger. Our mean-field analysis is confirmed by exact calculations, using Fock-space expansions. Finally, we fit experimental low temperature Feshbach sweep data with a power-law dependence. While the agreement with the experimental data is well within experimental error bars, similar accuracy can be obtained with an exponential fit, making additional data highly desirable.

Molecule formation in optical lattice wells by resonantly modulated magnetic fields

We present a theoretical model for formation of molecules in an optical lattice well where a resonant coupling of atomic and molecular states is provided by small oscillations of a magnetic field in the vicinity of a Feshbach resonance. As opposed to an adiabatic sweep over the full resonance, this provides a coherent coupling with a frequency that can be tuned to meet resonance conditions in the system. The effective Rabi frequencies for this coupling are calculated and simulations show perfect Rabi oscillations. Robust production of molecules with an adiabatic sweep of the modulation frequency is demonstrated. For very large oscillation amplitudes, the Rabi oscillations are distorted but still effective and fast association is possible.

Fermions in Optical Lattices Swept across Feshbach Resonances

We point out that the recent experiments at ETH on fermions in optical lattices, where a band insulator evolves continuously into states occupying many bands as the system is swept adiabatically across Feshbach resonance, have implications on a wide range of fundamental issues in condensed matter. We derive the effective Hamiltonian of these systems, obtain expressions for their energies and band populations, and point out the increasing quantum entanglement of the ground state during the adiabatic sweep. Our results also explain why only specific regions in k space can be populated after the sweep as found at ETH.

Thermodynamics of Interacting Fermions in Atomic Traps

We calculate the entropy in a trapped, resonantly interacting Fermi gas as a function of temperature for a wide range of magnetic fields between the BCS and Bose-Einstein condensation end points. This provides a basis for the important technique of adiabatic sweep thermometry and serves to characterize quantitatively the evolution and nature of the excitations of the gas. The results are then used to calibrate the temperature in several ground breaking experiments on (6)Li and (40)K.

A new technique for cross polarization in solid-state NMR compatible with high spinning frequencies and high magnetic fields

The idea of integrated cross polarization which has been utilized for electron-to-nucleus polarization transfer is applied to nucleus-to-nucleus polarization transfer. Instead of using a π 2 pulse followed by a π 2 phase-shifted locking pulse like in the conventional cross polarization, irradiation with a single phase is applied together with adiabatic frequency sweep from far off-resonance toward on-resonance. This is capable of locking individual spin packets even in the presence of considerable spectral distribution and/or line broadening. Thus, this technique can provide efficient polarization transfer for spin species having large chemical shifts and experiments in high static fields.

Nonlinear Adiabatic Passage from Fermion Atoms to Boson Molecules

We study the dynamics of an adiabatic sweep through a Feshbach resonance in a quantum gas of fermionic atoms. Analysis of the dynamical equations, supported by mean-field and many-body numerical results, shows that the dependence of the remaining atomic fraction Gamma on the sweep rate alpha varies from exponential Landau-Zener behavior for a single pair of particles to a power-law dependence for large particle number N. The power law is linear, Gamma is proportional to alpha, when the initial molecular fraction is smaller than the 1/N quantum fluctuations, and Gamma is proportional to alpha(1/3) when it is larger. Experimental data agree well with a linear dependence, but do not conclusively rule out the Landau-Zener model.

Production of three-body Efimov molecules in an optical lattice

We study the possibility of associating meta-stable Efimov trimers from three free Bose atoms in a tight trap realised, for instance, via an optical lattice site or a microchip. The suggested scheme for the production of these molecules is based on magnetically tunable Feshbach resonances and takes advantage of the Efimov effect in three-body energy spectra. Our predictions on the energy levels and wave functions of three pairwise interacting 85Rb atoms rely upon exact solutions of the Faddeev equations and include the tightly confining potential of an isotropic harmonic atom trap. The magnetic field dependence of these energy levels indicates that it is the lowest energetic Efimov trimer state that can be associated in an adiabatic sweep of the field strength. We show that the binding energies and spatial extents of the trimer molecules produced are comparable, in their magnitudes, to those of the associated diatomic Feshbach molecule. The three-body molecular state follows Efimov's scenario when the pairwise attraction of the atoms is strengthened by tuning the magnetic field strength.

Production Efficiency of Ultracold Feshbach Molecules in Bosonic and Fermionic Systems

We investigate the production efficiency of ultracold molecules in bosonic 85Rb and fermionic 40K when the magnetic field is swept across a Feshbach resonance. For adiabatic sweeps of the magnetic field, our novel model shows that the conversion efficiency of both species is solely determined by the phase space density of the atomic cloud, in contrast with a number of theoretical predictions. In the nonadiabatic regime our measurements of the 85Rb molecule conversion efficiency follow a Landau-Zener model.

A modified CRISIS-HSQC for band-selective IMPRESS

CRISIS (Compensation of Refocusing Inefficiency with Synchronized Inversion Sweep) is a powerful technique for obtaining multiplicity-edited HSQC spectra without compromising sensitivity. However, the stringent requirement for the duration of the CRISIS waveforms makes them unsuitable for other functions, such as band selection or IMPRESS (IMProved REsolution using Symmetrically Shifted pulses). We report here a modified CRISIS-gHSQC pulse sequence employing time-reversed 13C pi/2 EBURP-2 pulses. This IC-bs-gHSQC (IMPRESS-CRISIS-bs-gHSQC) sequence was found to be equally useful for acquiring multiplicity-edited, band-selective spectra individually or in tandem with IMPRESS. Remarkably, the latter provides multiple spectra in significantly less time and is the preferred approach when several crowded regions need to be assigned unambiguously. The use of adiabatic sweeps and the CRISIS pulses enable IC-bs-gHSQC to give better sensitivity than the original IMPRESS sequence for band-selective spectra.

Adiabatic pulses in 1H–15N direct and long‐range heteronuclear correlations

The application of adiabatic inversion pulses to the detection of (1)H-(15)N heteronuclear correlations is described. The pulse sequences studied were gHSQC, CRISIS-gHSQC, gHMBC and CRISIS-gHMBC. The poor inversion quality of rectangular 180 degrees X pulses can lead to a loss of signal at the peripheries of the spectrum. Replacing these pulses with adiabatic sweeps significantly improves sensitivity across the potentially large (15)N spectral window. Satellite spectrum profiles are shown to demonstrate the increase in sensitivity when employing adiabatic pulses on wide spectral widths. Additionally, the active pharmaceutical nizatidine was used as a model compound to demonstrate the improvements in the long-range correlation data.

Compensation of refocusing inefficiency with synchronized inversion sweep (CRISIS) in multiplicity-edited HSQC

Use of adiabatic pulses in broadband inversion and decoupling is well known. Replacement of the rectangular π pulses in the INEPT and rev-INEPT parts of the HSQC and gHSQC experiments with adiabatic pulses substantially improves the sensitivity of these experiments. However, modulation of cross peak intensity in multiplicity-edited HSQC or gHSQC experiments can be quite severe. These modulations arise during the multiplicity-editing periods due to the inefficient refocusing of the spin-echo caused by the mismatch of the echo delay with the one-bond coupling constant. These modulations (which we call echo modulations) are field strength (and hence spectral width) independent. Use of adiabatic pulses with the inversion sweep synchronized to the 1H– 13C coupling constant range typically observed in a 13C spectrum will provide substantial improvement in sensitivity. The inversion profile problems associated with rectangular π pulses can be moderately compensated by composite pulse schemes and these schemes could prove to be reasonable alternatives to adiabatic pulses. However, the adiabatic sweep provides a unique method to compensate the echo modulations for multiplicity-edited experiments. The origin and the compensation of refocusing inefficiency with synchronized inversion sweep (CRISIS) method to minimize these modulations is described.

Conversion of an atomic Fermi gas to a long-lived molecular Bose gas.

We have converted an ultracold Fermi gas of 6Li atoms into an ultracold gas of 6Li2 molecules by adiabatic passage through a Feshbach resonance. Approximately 1.5 x 10(5) molecules in the least-bound, v=38, vibrational level of the X1Sigma(+)(g) singlet state are produced with an efficiency of 50%. The molecules remain confined in an optical trap for times of up to 1 s before we dissociate them by a reverse adiabatic sweep.

Design of adiabatic logic for a quantum CNOT gate

We examine the realization of a quantum CNOT gate by adiabatic operations. The principles of such systems and their analysis are briefly discussed and a model consisting of two weakly coupled double-potential well qubits is studied numerically. Regions of the parameter space with suitable well-defined sets of wavefunctions are found, in which then an adiabatic sweep of an external bias produces the switching behavior of CNOT. Results are presented on the adiabatic condition and the identification with the parameters of a flux-coupled two-SQUID system is given. For typical parameters adiabatic times in the nanosecond regime are obtained.

Universal Equations for Linear Adiabatic Pulses and Characterization of Partial Adiabaticity

A numerical analysis of the sech/tanh (or hyperbolic secant) and tanh/tan adiabatic inversion pulses provides a set of master equations for each type of pulse that guarantee their optimal implementation over a wide range of practical conditions without needing to further simulate the inversion profiles of the pulses. These simple equations determine the necessary maximum RF amplitude (RFmax) required for a preselected degree of inversion across a chosen effective bandwidth (bweff) and for a chosen pulse length (Tp). The two types of pulse function differently: The sech/tanh pulse provides a rectangular inversion profile with bweff being a large fraction of the adiabatic frequency sweep (bwdth), whereas for tanh/tan bweff is ≤bwdth/20. If the quality of inversion is defined as the minimum allowable extent of inversion, ιbw, at the boundaries of bweff, two basic linear equations are found for both types of pulse and these are of the form (RFmaxTp)2=m1Tpbwdth+c1 and Tpbwdth=m3Tpbweff+c3. The different behavior of the two pulses is expressed as different dependencies of the slopes mn and intercepts cn on ιbw and allowances are made for second order effects within these equations. The availability of these master relationships enables a direct comparison of the two types of adiabatic pulse and it is found that tanh/tan requires about half the pulse length of an equivalent sech/tanh pulse and also has the advantage of being less sensitive to the effects of scalar coupling. In contrast sech/tanh delivers about half the total RF power of an equivalent tanh/tan pulse. It is expected that the forms of these two basic linear equations are generally applicable to adiabatic inversion pulses and thus define the concept of “linear adiabaticity.” At low values of Tpbwdth or Tpbweff the linear equations no longer apply, defining a region of “partial adiabaticity.” Normal adiabatic pulses in the middle of this partial region are more efficient in terms of RFmax or Tp but are moderately less tolerant to RF inhomogeneity. A class of numerically optimized pulses has recently been developed that specifically trades adiabaticity in an attempt to gain RFmax or Tp efficiency. In comparison to normal adiabatic pulses implemented under optimal conditions, these new partially adiabatic pulses show only marginal improvements; they are restricted to single values of Tpbweff, and they are vastly less tolerant to RF inhomogeneity. These comparisons, and direct comparisons between any types of inversion pulse, adiabatic or otherwise, can be made using plots of (RFmaxTp)2 or (Total Power) Tp versus Tpbweff.

Strange effects of pulse shaping in water presaturation experiments

During the course of some water presaturation experiments with a shaped pulse envelope we observed inverted responses from certain signals flanking the water response. This phenomenon did not occur when a rectangular presaturation envelope was used. Apparently the leading and trailing edges of the shaped pulse act as adiabatic sweeps, causing the coupled magnetizations in question to be spin-locked. This gives rise to Hartmann-Hahn coherence transfer, and when the spin lock duration is equal to 1/(2J) the trajectories are such as to carry these magnetization vectors to the -z axis, leading to inverted signals in the final spectrum. Copyright 2000 Academic Press.

A homonuclear spin-pair filter for solid-state NMR based on adiabatic-passage techniques

A filtering scheme for the selection of spin pairs (and larger spin clusters) under fast magic-angle spinning is proposed. The scheme exploits the avoided level crossing in spin pairs during an adiabatic amplitude sweep through the so-called HORROR recoupling condition. The advantages over presently used double-quantum filters are twofold. (i) The maximum theoretical filter efficiency is, due to the adiabatic variation, 100% instead of 73% as for transient methods. (ii) Since the filter does not rely on the phase-cycling properties of the double-quantum coherence, there is no need to obtain the full double-quantum intensity for all spins in the sample at one single point in time. The only important requirement is that all coupled spins pass through a two-spin state during the amplitude sweep. This makes the pulse scheme robust with respect to rf-amplitude missetting, rf-field inhomogeneity and chemical-shift offset.

Cross-polarization efficiency in INS systems using adiabatic RF sweeps

The theory describing nuclear magnetic resonance cross-polarization using adiabatic sweeps of the rf spin-lock fields through the Hartmann–Hahn matching condition is extended to small homonuclear coupled systems of the type INS. In particular, the connection is made between such experiments and the associated theoretical limits on polarization transfer—the “unitary bounds”—demonstrating that these techniques can achieve the maximum transfer of polarization from the I spins to the S spins, subject to the constraint of angular momentum conservation imposed by spin-locking. Factors such as permutation symmetry of the spins, imperfect adiabaticity of individual crossings and fast sample spinning are shown to have no fundamental impact on the validity of these results.