- 112 Views
- Uploaded on

Download Presentation
## Clock Shifts

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

### Clock Shifts

Sourish Basu

Stefan Baur

Theja De Silva (Binghampton)

Dan Goldbaum

Kaden Hazzard

Erich Mueller

Cornell University

Outline

- What we want to measure
- A tool: Doppler free spectroscopy
- Capabilities
- Challenges
- Probing fermionic superfluidity near Feshbach resonance

Take-Home Message

- RF/Microwave spectroscopy does tell you details of the many-body state
- Weak coupling -- density
- Strong coupling -- complicated by final-state effects
- Bimodal RF spectra in trapped Fermi gases not directly connected to pairing (trap effect)

Ketterle Group: Science 316, 867-870 (2007)

“Pairing without Superfluidity: The Ground State of an Imbalanced Fermi Mixture”

Context: Upcoming Cold Atom Physics

Profound increase in complexity

Ex: modeling condensed matter systems

Big Question:

How to probe?

What we want to know

- Is the system ordered? (crystaline, magnetic, superconducting, topological order)
- What are the elementary excitations?
- How are they related to the elementary particles?

Atomic Spectroscopy

I(w) [transfer rate]

E

w

w

w0

Narrow spectral line in vacuum: in principle sensitive to details of many-body state

Measured hyperfine linewidth ~ 2 Hz [PRL 63, 612, 1989]

Interaction energy in Fermi gas experiments: 100 kHz

Possibly very powerful

Sharp Spectral lines

Hyperfine spectrum: nuclear spin flips (cf. NMR)

“Forbidden” optical transitions: Hydrogen 1S-2S

Couple weakly to environment: influenced by interactions? Does internal structure of atom depend on many-body state?

(weak coupling)

(weak coupling)

Line shift proportional to density [Clock Shift]

Application -- Detecting BEC

BEC

Density bump

Spectrum gives histogram of density

Solid: condensedOpen: non-condensed

Exp: (Kleppner group) PRL 81, 3811 (1998)

Theory: Killian, PRA 61, 033611 (2000)

[OSU connection -- Oktel]

Why is density histogram useful?

Optical absorption: column density

obscures interesting features -- ex. Mott Plateaus -- digression

Bose-Mott physics

Optical lattice:

Kinetic energy from hopping dominates

Weak interactions: atoms delocalize -- superfluid

-- Poisson number distribution

Energy cost of creating particle-hole pair exceeds hopping

Strong interactions: suppress hopping -- insulator

RF Spectroscopy

Exp: Ketterle group [Science, 313, 649 (2006)]

Thy: Hazzard and Mueller [arXiv:0708.3657]

2

1

3

4

5

Spectral shift proportional to density

Discrete bumps: density plateaus

Sensitivity

Significant peaks, even in superfluid

Q: could this be used to detect other corrugations? FFLO? CDW?

Spatially resolved

Column densities

So simple?

Spectrum knows about more than density!

Jin group [Nature 424, 47 (2003)]

Ex: RF dissociation - Potassium Molecules

(Thermal, non-superfluid fermionic gas)

Free atoms

Initially weakly bound pairs in

(and free atoms in these states)

pairs

Drive mf=-5/2 to mf=-7/2

n [kHz]

Related workEx: RF dissociation - Lithium Molecules

B [Gauss]

All 1+2 atoms in molecular bound state

(note reversal of sign of shift)

Grimm group [Science 305, 1128 (2004)]Background: Ketterle group [Science 300, 1723 (2003)

What is probed by RF spectroscopy?

Single Component Bose system:

Excite with perturbation

Final state has Hamiltonian

Fermi’s Golden Rule

(pseudospin susceptibility)

Simple Limits I

Final state does not interact (V(ab)=0)

- analogous to momentum resolved tunneling (or in some limits photoemission)
- probe all single particle excitations

Initial: ground state

Final: single a-quasihole of momentum k single free b-atom

Example: BCS state -- darker = larger spectral density

w

w

k

k

Simple Limits II

Final state interacts same as initial (V(ab)=V(bb)), and dispersion is same

- Coherent spin rotation

Formally can see from X acts as ladder operator

General Case -- Sum Rule

Mehmet O. Oktel, Thomas C. Killian, Daniel Kleppner, L. S. Levitov,

Phys. Rev. A 65, 033617 (2002)

Mean clock shift

Ex: Born approximation point interaction

Problem

Not a low energy observable!!!!!! -- dif potentials = dif results

Tails dominate sum rule

(unmeasurable)

Pethick and Stoof, PRA 64, 013618 (2001)

Summary of spectroscopy

- Weak coupling
- peak mostly shifted (proportional to density)
- long tails (probably unobservable)
- final interaction = initial
- Peak sharp and unshifted
- General
- No simple universal picture
- sum rules are ambiguous
- Important for experiments on strongly interacting fermionic Lithium atoms

Lithium near Feshbach resonance

Innsbruck expt grp +NIST theory grp, PRL 94, 103201 (2005)

Strongly interacting superfluid

BCS-BEC crossover -- Randeria

Outline

(what is RF lineshape -- and what does it tell us)

- Homogeneous lineshapes within BCS model of superfluid
- Crude model for trapped gas
- Highly polarized limit (normal state)
- Demonstrates universality of line shape

Variational Model

Idea: include all excitations consisting of single quasiparticles quasiholes

“coherent contribution” -- should capture low energy structure

a-b pairs -- excite from b to c

Neglects multi-quasiparticle intermediate states

[Exact if (final int)=(initial int) or if (final it)=0]

Perali, Pieri, StrinatiarXiv:0709.0817

ExperimentKetterle group: Phys. Rev. Lett. 99, 090403 (2007)

Sant-Feliu update: has seen “bound-bound”

Summary: Homogeneous Lineshape

- Final state interactions crucial:
- Is there a bound state?
- Distorted spectrum if resonance in continuum
- Sets scale

Next: trap

Inhomogeneous line shapes

Most experiments show trap averaged lineshape

Grimm group, Science 305, 1128 (2004)

Bimodality:due to trap

Where spectral weight comes from

Massignan, Bruun, and Stoof, ArXiv:0709.3158

Edge of cloud

Calculation in normal state: Ndown<Nup

More particles at center

Highly polarized limit: only one down-spin particle

Generic propertiesAssumption: local clock shift =

(homogeneous spectrum peaks there)

High temp:

[Virial expansion: Ho and Mueller, PRL 92, 160404 (2004)]

High density:

Different a

Bimodality

nup

ndn

r

Center of trap: highest down-spin density -- gives broad peak

Edge of trap: low density, but a lot of volume

-- All contribute at same detuning

-- Gives power law singularity

Calculating Free Energy

(Only if asked)

If ndown is small, q is only function of mup and x=w-mup-mdn.

Arctan vanishes for negative x [so w is large]

Summary: Trap

- Trap leads to bimodal spectrum (model independent)
- Simple model using NSR energy: energy scales work, temp scales seem a bit off
- Final state interactions: mostly scale spectrum

Decreasing T/TF

Decreasing a/l

Summary -- Spectroscopy

- Powerful probe of local properties
- Density: SF-Mott
- Simple when interactions are weak
- Open Q’s when interactions are strong
- Bimodal RF spectra are not directly related to pairing (implicit in works of Torma and Levin)

Fin

Download Presentation

Connecting to Server..