Search Results (95 total)

Interference with atomic and molecular matter waves is a rich branch of atomic physics and quantum optics. It started with atom diffraction from crystal surfaces and the separated oscillatory fields technique used in atomic clocks. Atom interferometry is now reaching maturity as a powerful art with many applications in modern science. In this review the basic tools for coherent atom optics are described including diffraction by nanostructures and laser light, three-grating interferometers, and double wells on atom chips. Scientific advances in a broad range of fields that have resulted from the application of atom interferometers are reviewed. These are grouped in three categories: (i) fundamental quantum science, (ii) precision metrology, and (iii) atomic and molecular physics. Although some experiments with Bose-Einstein condensates are included, the focus of the review is on linear matter wave optics, i.e., phenomena where each single atom interferes with itself.

We present mathematical learning models—predictions of student’s knowledge vs amount of instruction—that are based on assumptions motivated by various theories of learning: tabula rasa, constructivist, and tutoring. These models predict the improvement (on the post-test) as a function of the pretest score due to intervening instruction and also depend on the type of instruction. We introduce a connectedness model whose connectedness parameter measures the degree to which the rate of learning is proportional to prior knowledge. Over a wide range of pretest scores on standard tests of introductory physics concepts, it fits high-quality data nearly within error. We suggest that data from MIT have low connectedness (indicating memory-based learning) because the test used the same context and representation as the instruction and that more connected data from the University of Minnesota resulted from instruction in a different representation from the test.

We investigate short-term learning from hints and feedback in a Web-based physics tutoring system. Both the skill of students and the difficulty and discrimination of items were determined by applying item response theory (IRT) to the first answers of students who are working on for-credit homework items in an introductory Newtonian physics course. We show that after tutoring a shifted logistic item response function with lower discrimination fits the students’ second responses to an item previously answered incorrectly. Student skill decreased by 1.0 standard deviation when students used no tutoring between their (incorrect) first and second attempts, which we attribute to “item-wrong bias.” On average, using hints or feedback increased students’ skill by 0.8 standard deviation. A skill increase of 1.9 standard deviation was observed when hints were requested after viewing, but prior to attempting to answer, a particular item. The skill changes measured in this way will enable the use of IRT to assess students based on their second attempt in a tutoring environment.

Elongated Bose-Einstein condensates (BECs) exhibit strong spatial phase fluctuations even well below the BEC transition temperature. We demonstrate that atom interferometers using such condensates are robust against phase fluctuations; i.e., the relative phase of the split condensate is reproducible despite axial phase fluctuations. However, larger phase fluctuations limit the coherence time, especially in the presence of some asymmetries in the two wells of the interferometer.

We have created a ⁸⁷Rb Bose-Einstein condensate in a magnetic trapping potential produced by a hard disk platter written with a periodic pattern. Cold atoms were loaded from an optical dipole trap and then cooled to Bose-Einstein condensation on the surface with radio-frequency evaporation. Fragmentation of the atomic cloud due to imperfections in the magnetic structure was observed at distances closer than 40  μm from the surface. Attempts to use the disk as an atom mirror showed dispersive effects after reflection.

The stability of superfluid currents in a system of ultracold bosons was studied using a moving optical lattice. Superfluid currents in a very weak lattice become unstable when their momentum exceeds 0.5 recoil momentum. Superfluidity vanishes already for zero momentum as the lattice deep reaches the Mott insulator (MI) phase transition. We study the phase diagram for the disappearance of superfluidity as a function of momentum and lattice depth between these two limits. Our phase boundary extrapolates to the critical lattice depth for the superfluid-to-MI transition with 2% precision. When a one-dimensional gas was loaded into a moving optical lattice a sudden broadening of the transition between stable and unstable phases was observed.

We present a quantum model of two-level atoms localized in a three-dimensional lattice based on the Hopfield polariton theory. In addition to a polaritonic gap at the excitation energy, a photonic band gap opens up at the Brillouin zone boundary. Upon tuning the lattice period or angle of incidence to match the photonic gap with the excitation energy, one obtains a combined polaritonic and photonic gap as a generalization of Rabi splitting. For typical experimental parameters, the size of the combined gap is on the order of 25  cm⁻¹, up to 10⁵ times the detuned gap size. The dispersion curve contains a branch supporting slow-light modes with vanishing probability density of atomic excitations.

The recombination of two split Bose-Einstein condensates on an atom chip is shown to result in heating which depends on the relative phase of the two condensates. This heating reduces the number of condensate atoms between 10% and 40% and provides a robust way to read out the phase of an atom interferometer without the need for ballistic expansion. The heating may be caused by the dissipation of dark solitons created during the merging of the condensates.

We measure the relative phase of two Bose-Einstein condensates confined in a radio frequency induced double-well potential on an atom chip. We observe phase coherence between the separated condensates for times up to ∼200  ms after splitting, a factor of 10 longer than the phase diffusion time expected for a coherent state for our experimental conditions. The enhanced coherence time is attributed to number squeezing of the initial state by a factor of 10. In addition, we demonstrate a rotationally sensitive (Sagnac) geometry for a guided atom interferometer by propagating the split condensates.

Continuous and pulsed quantum Zeno effects were observed using a ⁸⁷Rb Bose-Einstein condensate. Oscillations between two ground hyperfine states of a magnetically trapped condensate, externally driven at a transition rate ω_R, were suppressed by destructively measuring the population in one of the states with resonant light. The suppression of the transition rate in the two-level system was quantified for pulsed measurements with a time interval δt between pulses and continuous measurements with a scattering rate γ. We observe that the continuous measurements exhibit the same suppression in the transition rate as the pulsed measurements when γδt=3.60(0.43), in agreement with the predicted value of 4. Increasing the measurement rate suppressed the transition rate down to 0.005ω_R.

We study how interactions affect the quantum reflection of Bose-Einstein condensates. A patterned silicon surface with a square array of pillars resulted in high reflection probabilities. For incident velocities greater than 2.5  mm/s, our observations agreed with single-particle theory. At velocities below 2.5  mm/s, the measured reflection probability saturated near 60% rather than increasing towards unity as predicted by the accepted theoretical model. We extend the theory of quantum reflection to account for the mean-field interactions of a condensate which suppresses quantum reflection at low velocity. The reflected condensates show collective excitations as recently predicted.

We have observed parametric generation and amplification of ultracold atom pairs. A ⁸⁷Rb Bose-Einstein condensate was loaded into a one-dimensional optical lattice with quasimomentum k₀ and spontaneously scattered into two final states with quasimomenta k₁ and k₂. Furthermore, when a seed of atoms was first created with quasimomentum k₁ we observed parametric amplification of scattered atoms pairs in states k₁ and k₂ when the phase-matching condition was fulfilled. This process is analogous to optical parametric generation and amplification of photons and could be used to efficiently create entangled pairs of atoms. Furthermore, these results explain the dynamic instability of condensates in moving lattices observed in recent experiments.

Two spatially separate Bose-Einstein condensates were prepared in an optical double-well potential. A bidirectional coupling between the two condensates was established by two pairs of Bragg beams which continuously outcoupled atoms in opposite directions. The atomic currents induced by the optical coupling depend on the relative phase of the two condensates and on an additional controllable coupling phase. This was observed through symmetric and antisymmetric correlations between the two outcoupled atom fluxes. A Josephson optical coupling of two condensates in a ring geometry is proposed. The continuous outcoupling method was used to monitor slow relative motions of two elongated condensates and characterize the trapping potential.

We have used a microfabricated atom chip to split a single Bose-Einstein condensate of sodium atoms into two spatially separated condensates. Dynamical splitting was achieved by deforming the trap along the tightly confining direction into a purely magnetic double-well potential. We observed the matter wave interference pattern formed upon releasing the condensates from the microtraps. The intrinsic features of the quartic potential at the merge point, such as zero trap frequency and extremely high field-sensitivity, caused random variations of the relative phase between the two split condensates. Moreover, the perturbation from the abrupt change of the trapping potential during the splitting was observed to induce vortices.

A systematic shift of the photon recoil momentum due to the index of refraction of a dilute gas of atoms has been observed. The recoil frequency was determined with a two-pulse light grating interferometer using near-resonant laser light. The results show that the recoil momentum of atoms caused by the absorption of a photon is nℏk, where n is the index of refraction of the gas and k is the vacuum wave vector of the photon. This systematic effect must be accounted for in high-precision atom interferometry with light gratings.

We observed quantum reflection of ultracold atoms from the attractive potential of a solid surface. Extremely dilute Bose-Einstein condensates of ²³Na, with peak density 10¹¹–10¹²   atoms/cm³, confined in a weak gravitomagnetic trap were normally incident on a silicon surface. Reflection probabilities of up to 20% were observed for incident velocities of 1–8  mm/s. The velocity dependence agrees qualitatively with the prediction for quantum reflection from the attractive Casimir-Polder potential. Atoms confined in a harmonic trap divided in half by a solid surface exhibited extended lifetime due to quantum reflection from the surface, implying a reflection probability above 50%.

Doubly quantized vortices were topologically imprinted in |F=1⟩   ²³Na condensates, and their time evolution was observed using a tomographic imaging technique. The decay into two singly quantized vortices was characterized and attributed to dynamical instability. The time scale of the splitting process was found to be longer at higher atom density.

We demonstrate a Raman amplifier for matter waves, where the amplified atoms and the gain medium are in two different hyperfine states. This amplifier is based on a form of superradiance that arises from self-stimulated Raman scattering in a Bose-Einstein condensate.

Bose-Einstein condensates of sodium atoms, prepared in an optical dipole trap, were distilled into a second empty dipole trap adjacent to the first one. The distillation was driven by thermal atoms spilling over the potential barrier separating the two wells and then forming a new condensate. This process serves as a model system for metastability in condensates, provides a test for quantum kinetic theories of condensate formation, and also represents a novel technique for creating or replenishing condensates in new locations.

A new technique for maintaining high contrast in an atom interferometer is used to measure large de Broglie wave phase shifts. Dependence of an interaction induced phase on the atoms’ velocity is compensated by applying an engineered counterphase. The counterphase is equivalent to a rotation, is precisely determined by a frequency, and can be used to measure phase shifts due to interactions of unknown strength. Phase shifts of 150 rad (5 times larger than previously possible) have now been measured in an atom beam interferometer, and we suggest that this technique can enable comparisons of atomic polarizability with precision of one part in 10 000.

A trapped-atom interferometer was demonstrated using gaseous Bose-Einstein condensates coherently split by deforming an optical single-well potential into a double-well potential. The relative phase between the two condensates was determined from the spatial phase of the matter wave interference pattern formed upon releasing the condensates from the separated potential wells. Coherent phase evolution was observed for condensates held separated by 13   μm for up to 5 ms and was controlled by applying ac Stark shift potentials to either of the two separated condensates.

Coreless vortices were phase imprinted in a spinor Bose-Einstein condensate. The three-component order parameter of F=1 sodium condensates held in a Ioffe-Pritchard magnetic trap was manipulated by adiabatically reducing the magnetic bias field along the trap axis to zero. This distributed the condensate population across its three spin states and created a spin texture. Each spin state acquired a different phase winding which caused the spin components to separate radially.

Magnetically and optically confined Bose-Einstein condensates were studied near a microfabricated surface. Condensate fragmentation observed in microfabricated magnetic traps was not observed in optical dipole traps at the same location. The measured condensate lifetime was ≥20   s and independent of the atom-surface separation under both magnetic and optical confinement. Radio-frequency spin-flip transitions driven by technical noise were directly observed for optically confined condensates and could limit the condensate lifetime in microfabricated magnetic traps.

We have investigated the properties of Bose-Einstein condensates of sodium atoms in the upper hyperfine ground state. Condensates in the high-field seeking |F=2,m_F=-2⟩ state were created in a large volume optical trap from initially prepared |F=1,m_F=-1⟩ condensates using a microwave transition at 1.77 GHz. We found condensates in the stretched state |F=2,m_F=-2⟩ to be stable for several seconds at densities in the range of 10¹⁴   atoms/cm³. In addition, we studied the clock transition |F=1,m_F=0⟩→|F=2,m_F=0⟩ in a sodium Bose-Einstein condensate and determined a density-dependent frequency shift of (2.44±0.25±0.5)×10^-12   Hz cm³.

We have measured the index of refraction for sodium de Broglie waves in gases of Ar, Kr, Xe, and N₂ over a wide range of sodium velocities. We observe glory oscillations—a velocity-dependent oscillation in the forward scattering amplitude. An atom interferometer was used to observe glory oscillations in the phase shift caused by the collision, which are larger than glory oscillations observed in the cross section. The glory oscillations depend sensitively on the shape of the interatomic potential, allowing us to discriminate among various predictions for these potentials, none of which completely agrees with our measurements.