# Presentation: 534109

## Optical Measurement and Control

**Optical Measurement and Control**
**of Atomic Spin Ensembles**

## Thanks to

**UA**
**Kim Fook Lee**
**Brian Mischuck**
**Souma Chaudhury**
**W. Rakreungdet**
**Greg Smith**
**Lori Harrison**
**Kevin Schulz**

**Thanks to**

**NSF**

**ARO**

**UNM**
**Ivan Deutsch**
**Andrew Silberfarb**

## Basics: Atom-Probe Interactions

**Basics: Atom-Probe Interactions**

*atom*
*cloud*

**Typical setup**

**Off-resonance probe**

**dispersion only**

## Basics: Atom-Probe Interactions

**Basics: Atom-Probe Interactions**

**- what information about the system can we access?**
**- how does the probe affect the system evolution?**

## Basics: Atom-Probe Interactions

**Basics: Atom-Probe Interactions**

**- what information about the system can we access?**
**- how does the probe affect the system evolution?**

***atom-probe***
***interaction***

***field***

***atomic tensor polarizability***

***rank-2 tensor operator***
***acting in *****{*****F******g*****} *****manifold ***

## Basics: Atom-Probe Interactions

**Basics: Atom-Probe Interactions**

**- what information about the system can we access?**
**- how does the probe affect the system evolution?**

***Irreducible tensor ***
***decomposition***

***Scalar***

***spin & polarization-independent***

## {

**Basics: Atom-Probe Interactions**

**- what information about the system can we access?**
**- how does the probe affect the system evolution?**

***Irreducible tensor ***
***decomposition***

***Rotation of *****F, S***** around ******z******-axis***
***by angles ********** ******S******z ****** resp. ******F******z***

**Effect on spin:*****        rotation **********probe ellipticity***

**Effect on probe:*****      rotation ********** sample magnetization***

## Basics: Atom-Probe Interactions

**Basics: Atom-Probe Interactions**

**- what information about the system can we access?**
**- how does the probe affect the system evolution?**

***Irreducible tensor ***
***decomposition***

***Tensor***

**Effect on spin:*****        more general evolution***
***                           ******beyond rotations***

**Effect on probe:*****      change of ellipticity***
**                            ****(*****birefringence*****)**

## Basics: Atom-Probe Interactions

**Basics: Atom-Probe Interactions**

**- what information about the system can we access?**
**- how does the probe affect the system evolution?**

***Irreducible tensor ***
***decomposition***

**Alkali atoms in large detuning limit***** **********HF***

***nuclear spin decouples  ***

**We can measure only the components of   **

## Probing Spins by Faraday Rotation

***atom-probe coupling***

**Simple theory: Faraday signal**

***probe field***

***- no fictitious B-field -> no action on spins***
***- Faraday rotation of probe polarization***

**~ QND**
***measurement!***

## Probing Spins by Faraday Rotation

***index of refraction***

***angle of rotation***

***signal power***

**Simple theory: Faraday signal**

## Probing Spins by Faraday Rotation

***shot-noise equivalent power***

***smallest detectable spin***

***resolution limit***

**Simple theory: Shot-noise limited resolution**

***information gain***

## Probing Spins by Faraday Rotation

**Example: **
**    ****Larmor precession of Cs atoms in spin-coherent state**

***real-time, *****10****8*****atoms***

***SNR *****~ 470**

## Spin Squeezing by Measurement

**Compare resolution to Spin-Projection Noise**

***Collective spin***

***Mean-Square fluctuations***

***Spin-coherent state***

**Spin squeezing if**

***backaction***
***figure-of***
***-merit***

***Geremia et al, Science ***_**304,**_*** 270 *****(*****2004*****)*****, and next talk***

## Spin Squeezing by Measurement

***- optical pumping due to photon scattering*********
***- evolution of spin due to rank-2 tensor ***
***        ******part of atom-probe coupling***

*********d***** ~ *****few *****x***** ************s***

*********d***

***varies***
***widely***

## Spin Dependent Light Shift in Alkalis

***- keep terms to leading order ***
***           ******in *********HF********  ******

**Calculate total (vector+tensor) light shift @ finite ******** **

## Nonlinear Spin Dynamics

**Modified Larmor Hamiltonian***** ***
***  ******field B******x, ******probe pol. along x***

*theory*

***- Integrate Schrödinger eq.***
***         ******collapse & revival***

***- Master eq. treatment***

***- “non-linear” term ***
***         ******evolution *****≠***** rotation***

***Silberfarb & Deutsch***

**Modified Larmor precession**

## Nonlinear Spin Dynamics

**Modified Larmor Hamiltonian***** ***
***  ******field B******x, ******probe pol. along x***

***- Integrate Schrödinger eq.***
***         ******collapse & revival***

***- Master eq. treatment***

***- “non-linear” term ***
***         ******evolution *****≠***** rotation***

***Silberfarb & Deutsch***

**Modified Larmor precession**

***Experiment: collapse & revival ***
***              ******times versus ************s ****************s*****-1**

***- NL collapse MUCH faster -***
***than decoherence!***

## Controlling the Nonlinearity

***- nonlinear collapse limits***
***      ******useful measurement time***

***- measurement time limits***
***            ******backaction***

**Problem:**

***- we need some compensating***
***         ******nonlinear term***

***2nd NL light shift?***

***- in principle yes***

***- but there is a simpler way!***

## Controlling the Nonlinearity

**Experiment:***** play around with***
***                   ******geometry***

**How does it work?**

***nonlinear light shift***

**RWA**

***nonlinearity disappears for***

***probe geometry***

## Controlling the Nonlinearity

***collapse/dephasing vs angle***

***collapse/dephasing time vs ************s***
***        ******at “magic angle”***

## Summary: Probing Spins by Faraday Rotation 

***Smith, Chaudhury & Jessen***
***J. Opt. B ***_***5***_***, 323 (2003) ***

***- Tensor/nonlinear part of probe light shift important***
***                  ******collapse & revival in Larmor precession***
***- Backaction, spin squeezing limited by nonlinearity***
***- Nonlinearity can be cancelled***
***                ******useful measurement time***** ~ ****5-10 ***********s****** *****   **

***Smith et al. ***
***quant-ph/0403096 ***

## Outlook: Probing Spins by Faraday Rotation 

**Eliminate tensor/nonlinear light shift*****    ***
***   ******- recover QND measurement***
***   ******- long measurement times***
***                  ******backaction in moderate OD samples ***
**Enhance & use tensor/nonlinear light shift***** ***
***   ******- increase nonlinearity by tuning to D1 resonance***
**   ****- *****explore nonlinear spin dynamics (quantum chaos)***
***   ******- extract more general information***
***              ******real-time density matrix reconstruction***
***                     ******Silberfarb & Deutsch***
***   ******- implement more general measurements***
***                   ******probe clock doublet pseudospin***

**Outlook: Probing Spins by Faraday Rotation **

## Probing the Clock Doublet 

**Atomic clock doublet**
***probe & squeeze pseudospin?***
***atomic clocks, interferometers?***

## Probing the Clock Doublet 

**Problem:  *****no Faraday signal from m ********** states***

***Vector***

***clock***
***doublet***

**Answer:**

***Tensor***

***birefringence***

## Probing the Clock Doublet 

***Level scheme for Cs D1 transition***

## Probing the Clock Doublet 

***Level scheme for Cs D1 transition***

***- birefringence***

***upper clock state***

***- transparant***

***lower clock state***

## Probing the Clock Doublet 

**Net birefringent signal**

***Sensitivity comparable to***
***Faraday measurement ***

**Basic measurement setup**

- PBS

*9.2 GHz*

***- comparable performance -***

## Probing the Clock Doublet 

**Probing the Clock Doublet **

**Proof of principle:  *****measurement of Rabi Flopping***

***Theory: master eq. calc.***

***Exp: single-shot data***

***- it works! -***

- time (ms)

## Probing the Clock Doublet 

**Probing the Clock Doublet **

**Refinements:  *****designing a useful QND measurement***

**Problem: *****differential light shift ***
***               ******of clock states***

***inhomogeneous broadening ***
***of clock transition***

## Probing the Clock Doublet 

**Probing the Clock Doublet **

**Refinements:  *****designing a useful QND measurement***

**Solution: *****“magic” probe freq. ***
***                 ******where***

## Probing the Clock Doublet 

**Probing the Clock Doublet **

**Refinements:  *****designing a useful QND measurement***

*signal from*

*signal from*

*light shift*

- 4-4

- 4-3

- 3-4

- 3-3

***- “QND points” -***

## Probing the Clock Doublet 

**Probing the Clock Doublet **

**Refinements:  *****designing a useful QND measurement***

**Rabi flopping vs. probe frequency**

*Rabi freq.*

*decay time vs. ** *(***s** constant*)

***Master Eq. incl.***
***inhomogeneity***

***Exp.***

## Probing the Clock Doublet 

**Probing the Clock Doublet **

**Refinements:  *****designing a useful QND measurement***

**Problem:   *****signal measures ************z *****+ 1, *****not ************z***

*z*

*y*

*x*

**Angular momentum**

***squeezing independent ***
***     ******of***

**:)***** ***

## Probing the Clock Doublet 

**Probing the Clock Doublet **

**Refinements:  *****designing a useful QND measurement***

## Probing the Clock Doublet 

**Probing the Clock Doublet **

**Refinements:  *****designing a useful QND measurement***

## Probing the Clock Doublet 

**Probing the Clock Doublet **

**Refinements:  *****designing a useful QND measurement***

***appears feasible to design QND measurement ***
***of clock pseudospin in close analogy to***
***Faraday measurement of ang. momentum***
***- very similar measurement performance -***

## Application to Metrology 

**Ramsey Spectroscopy/Atomic Clocks (*****long shot*****)**

***S******z***

******/2 *****pulse***

***Ramsey***
***interrogation***

******/2 *****pulse***

***measure ******S******z***

****

***- details to be -***
***filled in***

## Application to Metrology 

***Map clock doublet onto atom interferometer paths***
**(*****Kasevich approach*****)**

***squeezed state***
***preparation***

***Raman ************  pulse***
***beamsplitter***

***Raman ************  pulse***
***beamsplitter***

***Raman ************  pulses***

***measure***
*********z***

***- details to be -***
***filled in***