Dynamics of a BEC colliding with a time-dependent dipole barrier OSA Frontiers in Photonics 2006 starring Chris Ellenor as Mirco Siercke Aephraim Steinberg’s group, University of Toronto

SUPPORT The Cold Atoms Crew Ringleader: –Aephraim Steinberg Postdoc: –Matt Partlow Grad Students: –Mirco Siercke, Samansa Maneshi, Chris Ellenor, Rockson Chang, Chao Zhang Observation of high-order quantum resonances in the delta kicked rotor Z4, 10:24 Saturday

Motivation Our long term goal is to study transit times for atoms tunneling through a potential barrier To begin, we will study predictions of non- classical behaviour in collisions with this barrier This effect suggests an interferometric method for measuring the condensate wavefunction / Wigner function

More localized = higher momentum components Consider an ensemble of particles with some distribution in phase space approaching a potential Classically, we can construct the inequality Quantum mechanically, this can be violated, and higher momentum components produced, i.e. G > 0 incomingoutgoing accumulated probability for momentum > p Collisional Transitory Enhancement of the High Momentum Components of a Quantum Wave Packet S. Brouard and J. G. Muga, Phys. Rev. Lett. 81, 2621–2625 (1998)

In our experiment we’ll use a small, weak barrier that barely causes any reflection of the BEC to look for these transient effects. (Brouard S., Muga J.G., Annalen der Physik 7 (7-8): ) Momentum distributions: We will switch the barrier off, let the BEC expand and get the momentum distribution from the time of flight Collisional transitory enhancement of the high momentum components

This effect can be easily understood by realizing that the barrier writes a Pi phaseshift onto the wavefunction The effect is a single-particle effect, so mean field energy present would make it impossible to use time of flight measurements to extract momentum distributions, and soliton formation would further complicate matters However: If we let the BEC expand first to get rid of mean field effects it will acquire a chirp (i.e. a quadratic phase profile)

Performing the experiment with an expanded BEC: TOF measurement of momentum distribution at time of collision Variable barrier position = variable drop time before collision 0 ms drop before collision

Performing the experiment with an expanded BEC: TOF measurement of momentum distribution at time of collision Variable barrier position = variable drop time before collision 1 ms drop before collision

Performing the experiment with an expanded BEC: TOF measurement of momentum distribution at time of collision Variable barrier position = variable drop time before collision 5 ms drop before collision

Performing the experiment with an expanded BEC: TOF measurement of momentum distribution at time of collision Variable barrier position = variable drop time before collision 12 ms drop before collision

One can think of the expanded BEC as a series of transform- limited wavepackets each with a different phase and velocity The fast wavepackets picked up a total phase of pi, the slow ones no phase, and only the central one exhibits transient enhancement of momentum This is analogous to SPIDER

The fringes then tell us the phase difference between the central momentum component and the rest of the cloud, allowing reconstruction of the wavefunction Because our barrier size is currently still large we expect to see asymmetric fringes:

AOM The Dipole Barrier – Making a Sheet of Light AOM scans beam Cylindrical telescope Absorption probe Spot is 8um thick by 200um wide With scan - sheet is ~ 0.5mm wide Height is ~ 150nK Intensity flat to < 1% 300 GHz detuned laser diode FPGA BEC of about Rb atoms

Some preliminary data –5.6ms expansion before collision, 15ms expansion after

Do we have an interferometer? Well, vary the phase! We notice from our data that fringes translate as a function of phase shift from the barrier

To understand this, consider the Fourier transform of our symmetric envelope with a discontinuous phase profile

Comparing to numerical models

Summary During the collision of a wavepacket with a barrier transient effects can be observed that are not visible in the asymptotic scattering limits. We may realize an interferometric effect similar to SPIDER where we infer phase information, and perhaps the Wigner function of our BEC using these transient effects Preliminary results have been achieved, possibly demonstrating a new method for extraction of phase information from a condensate Possible applications to BEC tomography, and study of entanglement evolution

The Experiment atoms dipole barrier We have a BEC of about Rb atoms Current efforts in the lab –Design and preparation of a 1D dipole trap –Improvements on barrier (imaging, size, control, etc.) –Overall stability of experiment