High sensitivity phonon spectroscopy of Bose-Einstein condensates using matter-wave interference

We study low momentum excitations of a Bose-Einstein condensate using a novel matter-wave interference technique. In time-of-flight expansion images we observe strong matter-wave fringe patterns. The fringe contrast is a sensitive spectroscopic probe of in-trap phonons and is explained by use of a Bogoliubov excitation projection method applied to the rescaled order parameter of the expanding condensate. Gross-Pitaevskii simulations agree with the experimental data and confirm the validity of the theoretical interpretation. We show that the high sensitivity of this detection scheme gives access to the quantized quasiparticle regime.Comment: 5 pages, 5 figures, author list update

Echo spectroscopy of bulk Bogoliubov excitations in trapped Bose-Einstein condensates

We propose and demonstrate an echo method to reduce the inhomogeneous linewidth of Bogoliubov excitations, in a harmonically-trapped Bose-Einstein condensate. Our proposal includes the transfer of excitations with momentum +q to -q using a double two photon Bragg process, in which a substantial reduction of the inhomogeneous broadening is calculated. Furthermore, we predict an enhancement in the method's efficiency for low momentum due to many-body effects. The echo can also be implemented by using a four photon process, as is demonstrated experimentally.Comment: 4 pages, 5 figure

Direct observation of the phonon energy in a Bose-Einstein condensate by tomographic imaging

The momentum and energy of phonons in a Bose-Einstein condensate are measured directly from a time-of-flight image by computerized tomography. We find that the same atoms that carry the momentum of the excitation also carry the excitation energy. The measured energy is in agreement with the Bogoliubov spectrum. Hydrodynamic simulations are performed which confirm our observation.Comment: Letter, 5 figure

Quantitative imaging of dielectric permittivity and tunability with a near-field scanning microwave microscope

We describe the use of a near-field scanning microwave microscope to image the permittivity and tunability of bulk and thin film dielectric samples on a length scale of about 1 micron. The microscope is sensitive to the linear permittivity, as well as to nonlinear dielectric terms, which can be measured as a function of an applied electric field. We introduce a versatile finite element model for the system, which allows quantitative results to be obtained. We demonstrate use of the microscope at 7.2 GHz with a 370 nm thick barium strontium titanate thin film on a lanthanum aluminate substrate. This technique is nondestructive and has broadband (0.1-50 GHz) capability. The sensitivity of the microscope to changes in relative permittivity is 2 at permittivity = 500, while the nonlinear dielectric tunability sensitivity is 10^-3 cm/kV.Comment: 12 pages, 10 figures, to be published in Rev. Sci. Instrum., July, 200

Absence of Anomalous Tunneling of Bogoliubov Excitations for Arbitrary Potential Barrier under the Critical Condensate Current

We derive the exact solution of low energy limit of Bogoliubov equations for excitations of Bose-Einstein condensate in the presence of arbitrary potential barrier and maximum current of condensate. Using this solution, we give the explicit expression for the transmission coefficient against the potential barrier, which shows partial transmission in the low energy limit. The wavefunctions of excitations in the low energy limit do not coincide with that of the condensate. The absence of the perfect transmission in the critical current state originates from local enhancement of density fluctuations around the potential barrier.Comment: 4 pages, 1 figur

Bogoliubov spectrum and Bragg spectroscopy of elongated Bose-Einstein condensates

The behavior of the momentum transferred to a trapped Bose-Einstein condensate by a two-photon Bragg pulse reflects the structure of the underlying Bogoliubov spectrum. In elongated condensates, axial phonons with different number of radial nodes give rise to a multibranch spectrum which can be resolved in Bragg spectroscopy, as shown by Steinhauer {\it et al.} [Phys. Rev. Lett. {\bf 90}, 060404 (2003)]. Here we present a detailed theoretical analysis of this process. We calculate the momentum transferred by numerically solving the time dependent Gross-Pitaevskii equation. In the case of a cylindrical condensate, we compare the results with those obtained by linearizing the Gross-Pitaevskii equation and using a quasiparticle projection method. This analysis shows how the axial-phonon branches affect the momentum transfer, in agreement with our previous interpretation of the observed data. We also discuss the applicability of this type of spectroscopy to typical available condensates, as well as the role of nonlinear effects.Comment: 8 pages, 7 figures, minor changes, typos correcte

Bragg spectroscopy with an accelerating Bose-Einstein condensate

We present the results of Bragg spectroscopy performed on an accelerating Bose-Einstein condensate. The Bose condensate undergoes circular micro-motion in a magnetic TOP trap and the effect of this motion on the Bragg spectrum is analyzed. A simple frequency modulation model is used to interpret the observed complex structure, and broadening effects are considered using numerical solutions to the Gross-Pitaevskii equation.Comment: 5 pages, 3 figures, to appear in PRA. Minor changes to text and fig