# Presentation: 119297

## What Do High Tc Superconductors Teach Us About Ultracold Superfluids and Vice Versa?

**Fermi  National Laboratory**

**Jan 2007**

**Notes:**
Emphasize exciting and important -- cold atom and high Tc

## Cold Atom Collaborators:Qijin Chen (Johns Hopkins, UC)

**J. Stajic  (U Chicago; LANL)**
**Yan He (U. Chicago)**
**ChihChun Chien (U. Chicago)**
_**J.E. Thomas,**_** J. Kinast, A. Turlapov (Duke)**
_**D.S. Jin**_**, C. Regal and M. Greiner (JILA)**
_**M. Holland**_**, M. Chiofalo, J. Milstein(JILA)**

## Impact of Superfluidity and Superconductivity

***2007 is 50 th anniversary of BCS Theory!***

*Festivities planned in Urbana  for coming October*

## Superfluidity Associated with at Least Eight Nobel Prizes 

**8 Nobel prizes** :
**1913 Onnes for superconductivity-expt**
**1972 Bardeen, Cooper, Schrieffer (BCS)-theory**
**1987 Bednorz and Muller– high Tc- expt**
**2001 BEC in trapped Bose gases-expt**
**2003 Abrikosov, Leggett, Ginzburg- theory**
**......****..**
**And Still counting !**

## Impact on Other Subfields of Fermionic Superfluidity

**Pairing in Nuclear Physics– Bohr, Mottelson, Pines.**
**Higgs mechanism in Particle Physics.**
**Dense QCD, color superconductivity in RHIC**
**Hadronic superfluidity in neutron stars**_**.**_
**Applications to accelerator physics.**

## The Essence of Fermionic Superfluidity

***fermions***

***bosons***

**Attractive interactions  turn fermions into “composite bosons****” (or ****Cooper pairs).**

***These are then driven by statistics to Bose condense.**** *

***Increased attraction***

## What is this talk about ?

**1.****   BCS theory and Bose Condensation (BEC) can be treated in one “master” theory (of fermion superfluids) with continuous evolution from one to another.**
**2.****    Ultracold gases are the best way to see this evolution.**
**3.****    But the same phenomenon may be present in high Tc cuprates.**

## Remarkable Tuning Capability  in Cold Gases via Feshbach Resonance

- .

**Scattering length**

**BCS**

**BEC**

*Unitary limit*

## Ultracold Fermi Gases

**Tuning the attractive interaction via Magnetic Field allows us to study**
**1. Most general form of fermionic superfluidity.**
**2. Unitary scattering prototypes for other subdisciplines.**

**BEC**

**BCS**

**Strong attraction**

**Weak attraction**

## High Tc Cuprates– also candidates for BCS-BEC Crossover

**BEC**

**BCS**

**“****The size of the cuprate pairs (from 10-30         puts us in the intermediate regime of the so-called **_**BCS-BEC crossover**_**” ****A. J. Leggett 2006 (Nature Physics).**
**                 ****See Also           ****T. D. Lee**** ****in 1987.**

## Three Part Talk

**Ground-breaking experiments in cold gases.**
**Theory interlude.**
**Expts. on **_**novel**_**, common  aspects of cold gases and high Tc cuprates.**

##  Part 1:   Proving SuperfluidityMuch easier on the Bose side of resonance!

* ***Observation of BEC in Fermi gases first reported by Jin et al, Nature 426  (2003).**
_**Simultaneously**_** by  Grimm et al, Science 302   (2003).**

## First Generation Evidence forsuperfluidity of Unitary gases:  early 2004:Phase Diagram  from JILA 

- .

***Based on rapid sweep to Bose gas regime.***

*Jin et al, PRL 92*

## Sweep Basis for Jin’s experiments

- .

***BCS***

***BEC***

*Unitary limit*

**Adiabatic sweep (sets temperature)**

**Quick sweep*** *

## Second Generation Experiments; Thermodynamical Evidence for Phase Transition near unitarity

- .

*Our Collaboration with Duke Group: John Thamas, Joe Kinast, Andrey Turlapov--- Feb 2005*

**Science 307, 1296 **

## Third Generation Experiments  Vortices Seen at  MIT-- April 2005

***Vortices “visible” after sweep to  BEC because of density depletion at the core.***

*Zwierlein et al , Nature 435, 170404 (2005)*

## Part 2     THEORY INTERLUDE: BCS, BEC and BCS-BEC Crossover

## What is Ground State for BCS-BEC Crossover ?

**Chemical potential varies when attraction  strength tuned arbitrarily: **

**Same as in BCS:**

## What is Novel about BCS-BEC Crossover?  Answer:  Finite T effects 

**Pairs form at one temperature  T***
**Pairs condense at lower temperature  Tc**
**New form of condensate excitation—pair excitations**

## What is special about BCS Theory?

**Pairs form and condense at the **_**same**_** temperature Tc**

**And this special case works magnificently, **_**except for high Tc cuprates!**_

##  More Rationale for Applying BCS-BEC Crossover to high Tc

**“****Pseudogap” (normal state gap) visible**.

**Compare with BCS: **

**Cuprates:**

## Statistical Basis of  Ideal Bose Condensation (BEC)

**Number Equation**
**Zero chemical Potential**
**Noncondensed bosons**

***.......................................******.***

***Number of condensed bosons               then determined.****     *

**Notes:**
Remember how we introduced the physics of BEC.  There is a close relation to our theory of BEC-BCS crossover.  Now we focus on the bosonic degrees of freedom through \Delta. Determine the condensate by subtraction.

## BCS-BEC Crossover Theory

**Pair chemical potential**:
**Total ``number” of pairs**
**Noncondensed pairs**:

***.......................................******.***

_***Composite bosons***_

_***Ideal Point bosons***_

***Leads to BCS gap equation for  ***

**Notes:**
Remember how we introduced the physics of BEC.  There is a close relation to our theory of BEC-BCS crossover.  Now we focus on the bosonic degrees of freedom through \Delta. Determine the condensate by subtraction.

## Part 3:The Unitary Gas: Looking for the Novel Form of Superfluidity: Via pseudogap effects and pair excitations

## Backdground: what goes on inside a trap?

**Particle density peaked at trap center**.
**Gap decreases from center to edge: bosonic excitations in middle, fermionic excitations at edge**.

## Density Profiles  and Pseudogap Effects

**Condensate**  **Noncondensed pairs**   **Fermions**

**Pair excitations **** smooth out profiles—making it hard to tell if system is normal or superfluid***. *

**PRL 95, 260405 (2005)**

**Notes:**
This slide first summarizes our collaboration with the Duke group. We calculated E vs T, They measured E vs an effective T. They didn’t know what physical T is – so they “read it from the density profiles” .. We sent them our theory profiles to calibrate their procedure. Don’t need TF.

## Thermodynamics and Pseudogap effects

**                                     ****Theory and expt**.

**In data, T* appears as temperature where 2 curves meet **

**Duke data**

_**Energy vs  T**_

**Science 307, 1296 (2005)**

##  RF Spectroscopy and Pseudogap Effects 

***ntermediate T***

***C. Chin et al, Science 305, 1128 (2004).***

***Temperature scale set by theory****** ***

## Latest Excitement: Fermionic Superfluidity 

**Latest Excitement: Fermionic Superfluidity **
**with****Imbalanced Spin Populations**

**Two groups: Rice and MIT**

## Rationale for the interest

**Interest from other sub-fields of physics:**
**               ****-(QCD) dense quark matter**
**               ****-inside neutron stars**
**               ****-nuclear physics**
**Search for the elusive Fulde Ferrell-****Larkin Ovchinnikov (FFLO) phase**
**                ****- Another “holy grail” in condensed matter**
**        **

## Population Imbalance Phase Diagram at Unitarity

- .

**In “****Sarma****” phase, polarization is in normal k-space region****.**
**                  **_**See related F. Wilczek papers**_**.                             **

**pg=pseudogap**

**PS=**** ****phase separation**** Polarization is in Fermi gas  outside superfluid core.**

**Experiments at MIT and Rice  seem to confirm  this phase diagram. **

## Last But Not Least.....BCS-BEC Crossover and High Tc Cuprates

## Cuprate Phase Diagram

**Apply crossover theory to *****d*****-wave latttice case**

***Theory ***

***Fit T*(x)***

**Pairs localize and Tc vanishes well before BEC.**

**Notes:**
We have looked at lots of comparisons. Forget AFM.  Here I just want to emphasize the phase diagram. .. Imagine you do crossover theory for the d-wave (lattice) case.  What will find?  The dotted line is T*..  Mention the d-wave and lattice effect which kills Tc.

##  Evidence for pair excitations in  underdoped cuprates

**.**

**Note that fermionic gap is highly non-universal**

**Theory**

**Understanding universality in Penetration depth vs temperature.**

**UBC experiments**

## Conclusions

-  **Cold gases present  opportunity to explore bigger-than-BCS theory (ie., rewrite the texts), **
**Possibly relevant to high Tc, **
**Strong interest from other subdisciplines**
**Future: More “exotic” phenomena in cold gases:**
**           ****1.  With optical lattices can test Hubbard models, RVB,...**
**          ****2.  Lots yet to explore in  population imbalance expts.  **
**                ****May find the FFLO?**
**   **
**   **
**    **

## Comparison with Rice data

**Density**

**Difference**

- Note polarization partly carried by noncondensed pairs = pseudogap effect.

**Rice Expt**

**Theory**

## Comparison with Rice data

- .

- Theory

- Rice data

## Comparison with MIT Data

- .

*Experiment*

*Theory*

## Comparison with Rice data –near unitarity

- .

**density**

**difference**

**Note polarization appears just outside superfluid core.**

**expt**

**theory**

## Comparison with MIT  at          in the near- BEC

- .

**MIT data**

**Above Tc**

**Below Tc**

**See clear signatures of superfluidity!**

**theory**