# Courses

## 1 Day Course

### Prof. Dr. Alexander Fetter

Stanford University

PDF documents:

07th May 2015 Synthetic gauge fields in Bose-Einstein Condensates

07th May 2015 Vortices in superfluid Helium and BEC

Courses

### **07th May 2015, Room D326**

**Title: "Vortices in superfluid Helium and BEC"**

I review the basic physics of superﬂuid ^{4}He, especially quantized vortices, and then describe dilute quantum gases, particularly Bose-Einstein condensates (BECs). The dynamical motion of an oﬀ-axis single vortex in a BEC provides a clear test of theoretical predictions; experiments conﬁrm these ideas in considerable detail at the 5-10% level. I review various experiments that create and detect vortices in BECs.

With increasing external rotation of the condensate, the BEC has many vortices, typically arranged in a triangular lattice. If the vortices are well separated, a simple mean-ﬁeld description suﬃces. For more rapid rotation, the vortex cores start to overlap, and a “lowest-Landau-level” picture becomes appropriate; it includes the local variation of the particle density.

For suﬃciently rapid rotation, the system is predicted to undergo a quantum phase transition to a highly correlated state, similar to a bosonic analog of the Laughlin 1/3 state for the fractional quantum Hall state of an electron gas in a strong magnetic ﬁeld. Such a correlated state would not have a condensate wave function and hence would not be superﬂuid. This transition has not yet been observed, but it would be highly interesting.

**07th May 2015, Room D326**

**Title: "Synthetic gauge fields in Bose-Einstein Condensates" **

I review the physics of two-component trapped spin-orbit coupled Bose Einstein condensates as created by the NIST group. Speciﬁcally, I focus on the dynamics of a vortex in such a two-component condensate.

I then consider synthetic gauge ﬁelds in optical lattices, dealing with three particular mechanisms: (1) time-dependent modulations (“shaken lattice”),

(2) laser-assisted tunneling to create Harper-Hofstadter square two-dimensional lattice in an applied magnetic ﬁeld with ﬂux ∼ 1/2 per plaquette, and (3) synthetic dimensions involving internal atomic states. In each case, I explain the synthetic vector potential and the associated complex phase of a hopping amplitude in the tight-binding Hamiltonian.

## 2 Days Course

### Dr. Jason Hogan

Stanford University

PDF documents:

23rd January 2014

28th January 2014

30th January 2014

Courses

### **23rd January 2014, Room D326**

**Title: "Precision atom interferometry in a 10 meter tower"**

Abstract: Light pulse atom interferometers measure inertial forces with high precision and accuracy, admitting many applications in both basic and applied science. Even after more than two decades of development, there are still opportunities for substantial increases in sensitivity, and ongoing work around the world aims to take advantage of these enhancements to realize new tests of fundamental physics, including tests of general relativity, measurements of fundamental constants, and detection of gravitational waves. Towards this end, I will describe atom interferometry performed in our 10 meter drop tower. Taking advantage of the long drop times available in this apparatus, we achieved a record interferometer duration of 2T = 2.3 seconds and a peak atom wavepacket separation of 1.4 cm. I will detail a number of the enabling techniques that we use including delta kick cooling, optical lattice acceleration, and Earth rotation compensation. I will also talk about our work developing large momentum transfer atom optics that increase the atom wavepacket separation towards 10 cm and beyond. In addition to substantially increasing the sensitivity, these demonstrations serve as a test of quantum mechanics by pushing the atom wavepacket separation into a new, macroscopic regime.

**30th January 2014, Room D326**

**Title: "Tests of fundamental physics using atom interferometry"**

Abstract: The high sensitivity achievable with atom interferometry enables new precision tests of fundamental physics. In particular, I will focus on various tests of general relativity that can be done using atoms, including testing the equivalence principle. I will describe our work towards setting new limits on the equivalence principle using a comparison between freely-falling Rb-85 and Rb-87 atoms in a 10 meter drop tower. I also will review prospects for gravitational wave detection using atom interferometry. Gravitational wave astronomy will provide a new window into the universe, collecting information about astrophysical systems and cosmology that is difficult or impossible to acquire using optical telescopes. I will present several proposed antenna designs based on freely-falling atoms, including terrestrial and space detectors. Atom interferometry offers a number of advantages, including access to conventionally inaccessible frequency ranges and substantially reduced antenna baselines. I will also explain how atomic physics techniques make it possible to build a gravitational wave detector with a single linear baseline, potentially offering advantages in cost and design flexibility.

## 4 Days Course

### Prof. Dr. Kurt Gibble

Penn State University, Department of Physics

Lectures:

### Wednesday, 28. August 2013, 09:00 - 12:00 h, Room D326

**Teaching and mentoring in precision measurements with clocks and interferometers and in building ultra-stable lasers **

Nearly all of what you need from quantum scattering theory for atom-interferometers, atomic clocks, and ultra-cold gas experiments. The first lecture will give a review of the foundations of the interactions between ultra-cold atoms needed for atom-interferometers, atomic clocks, and quantum gas experiments. Beginning with quantum scattering theory, we will build a practical understanding of scattering with discussions of the traditional formal theory and some novel examples. Key results are density dependent frequency shifts in clocks and atom-interferometers, atom-atom interaction shifts in traps, and thermalizing collisions in traps.

### Wednesday, 04. September 2013, 09:00 - 12:00 h, Room D326

**Precision Measurements of Scattering Phase Shifts in a Fountain Clock **

A series of experiments will be presented that elucidate quantum features of atom-atom scattering. This series lead to a new type of scattering experiment that allows us to directly observe scattering phase shifts as the phase shift of Ramsey fringes in an atomic clock. The technique gives unambiguous differences of scattering phase shifts that are independent of the atomic density to lowest order, enabling scattering phase shift measurements with clock-like accuracy. Recently, we have observed the rapid variations of scattering phase shifts as we tune the collision energy through Feshbach resonances. Such measurements will accurately test and constrain our knowledge of cesium-cesium interactions. Future measurements using this technique may place stringent limits on the time variation of fundamental constants, such as the electron-proton mass ratio.

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Lab Tutorials:

### 09. September 2013, 09:00 - 12:00, Room D32

**s-wave Frequency Shifts and Spin Waves in Fermion Clocks **

We observe the s-wave frequency shifts of fermions in a clock. Ultracold Fermions suppress collisions because identical fermions cannot interact as the temperature approaches zero, and thus fermions are attractive candidates for optical lattice clocks. Excitation inhomogeneities allow fermions to become somewhat distinguishable and therefore ultracold Fermion clocks can have collisional frequency shifts. The fermion shifts behave differently than those for bosons. We observe the distinguishing characteristics and spin-waves, which we show are inextricably connected. We discuss models to understand the shift and present clock experiments with fermions and bosons, 6Li and 87Rb. We will also discuss strong interactions, which yield long coherence times and suppress the s-wave collision shift.

### 23. September 2013, 09:00 - 12:00, Room D32

**Recent advances and the state-of-the-art of fountain clocks**

The understanding of the limiting systematic errors in laser-cooled microwave clocks has substantially improved in the last few years.

Rigorous evaluations of the systematic errors due to first order Doppler shifts in microwave cavities, the microwave lensing of atomic wavepackets, and background gas collisions has reduced the inaccuracy of the clocks that keep atomic time by a factor of two. We will discuss the physics of the Doppler shifts and microwave lensing, and the current limitations to the clock accuracies. We also discuss an alternative and highly uniform state selection technique. It is expected to be important for the microgravity clock PHARAO on ACES, and can also be applied to fountain clocks.

## 3 Days Course

### Prof. Dr. Franck Pereira Dos Santos

Centre National de la Recherche Scientifique (CNRS)

Thursday: 02th May 2013, 10:00 - 12:00 h, Room D 326

Monday: 06th May 2013, 10:00 - 12:00 h, Room C 109

Wednesday: 08th May 2013, 10:00 - 12:00 h, Room C 109

**Atom Interferometry**

Wave-particule duality postulates that a wave-packet (a de Broglie wave) can be associated to each particle, which can then be manipulated in the same way as light in optics. Atomic wave-packets can for example be split or recombined, allowing them to interfere. In an atom interferometer, the splitting between the two partial wave-packets associated to the same atom gives an extremely high sensitivity to inertial forces as acceleration and rotation. The use of laser cooled atomic samples enables increasing drastically the measurement time and thus the sensitivity. One of the interests of atom interferometry arises from its ability to provide very stable and accurate measurements, which are required for use in various fields of application, such as inertial navigation, geophysics or fundamental physics.

I will start by a brief historical review of the field, from the very first demonstrations of the wave character of matter to modern and state of the art instruments. I will present the many interferometer configurations that have been demonstrated, as well as their applications. I will focus on the description of laser based interferometers, where beamsplitters are realized with laser pulses, which allow for the realization of highly sensitive and accurate sensors. In particular, I will discuss Raman lasers based inertial sensors, where the interferometer is performed on free falling cold atoms. I will give details on the limits in the performances of these instruments, which have reached performances comparable to state of the art classical instruments, both in terms of sensitivity and accuracy. I will also present more prospective geometries, based on trapped geometries, as well as ambitious large scale instruments.