# Presentation: 816369

## Tackling the challenges of quantum computing with trapped ions

- Paul C. Haljan
- Monroe Group
- University of Michigan

- QUEST 2004
- Santa Fe

## Cd+

- Cd+

## Physics Today

- March, 2004

## Building a quantum computer:

- qubits

- controlled
- coupling

- ... to >99% accuracy*

- * provided things have been done right

- 				a reductionist’s view

- Prime target Hamiltonians: strongly interacting many-body systems
- e.g. Bose Hubbard model, Quantum Hall systems

## Ion Trap QC Groups

- Aarhus (Ca+)
- Almaden(IBM) (Ba+)
- Hamburg (Yb+)
- Innsbruck (Ca+)
- Los Alamos (Sr+)
- McMaster (Mg+)

_**Ion Trap QC Groups**_

- Several Cd isotopes – useful
- eg Sympathetic cooling: B.Blinov et al. PRA 65, 040304R (2002)

**Michigan (Cd****+****)**
- MPQ Munich (In+, Mg+)
- NIST-Boulder (Be+)
- NPL Teddington (Sr+)
- Oxford (Ca+)

## Photoionization-loading of Cd+ into trap

- Photoionization-loading of Cd+ into trap

- laser center wavelength (nm)

- 0

- 1

- 2

- 3

- laser
- bandwidth

- Cd 1S0  1P1
- transition

- pulsed laser
- (80 MHz, 2 psec, Pavg1 mW)
- Next: narrow BW laser for isotope selectivity!

- 1S0

- 1P1

- continuum

- 229nm

- 229nm

- Cd+ loading
- rate (sec-1)

## 111Cd+ atomic structure (113Cd+ similar)

- 111Cd+ atomic structure (113Cd+ similar)

- 1,1

- 1,0

- 1,-1

- 0,0

- 215nm

**2****S****1/2**

**2****P****1/2**

**2****P****3/2**

- 74 THz

- 14.53 GHz

- magnetic insensitive
- qubit (to 2nd order)
-   (600 Hz/G2)·B·B

**|******

**|******

- 226nm

## 2S1/2

**2****S****1/2**

- 14.53 GHz

**|******

**|******

**2****P****3/2**

- Near perfect initialization (optical pumping)

- /2 = 50 MHz

## 2S1/2

**2****S****1/2**

- 14.53 GHz

**|******

**|******

**2****P****3/2**

- Photon count in 0.2ms

- Efficient state detection: **|******** = **“bright”

- cycling

- Prob.

## |

- 14.53 GHz

**|******

**|******

**2****P****3/2**

**Far from**
**resonance**

- Photon count in 0.2ms

- Prob.

- 99.7% discrimination
- between **|****** and **|******

- Efficient state detection: **|******** = **“dark”

## |

- 14.53 GHz

**|******

**|******

**2****P****3/2**

- Qubit operations: optical Raman transitions

**2****P****1/2**

- 74 THz

- Large

- (microwaves also useful)

## Practical trap designs 

*3-layer linear trap*
-  Trapping of ion strings
- 3-layer geometry allows multiplexing, T-junctions, etc.

*Ring-and-fork quadrupole trap*
-  easy to build, good for testing

## Tee junction 

- Top layer of 9-zone, 49 electrode
- “Tee” junction trap.
- Short term goal: shuttling operations

- entangle

- shuttle

- entangle

- M. Acton
- D. Stick
- J. Sauer (REU)
- W. Hensinger
- J. Rabchuk

## Dan Stick

- Martin Madsen
- Winfried Hensinger
- Keith Schwab (LPS/UMd)

## 6m

- 6m

- 40m

## Single qubit operations: Rabi and Ramsey oscillations

**P(********)**

- ion

- Copropagating
- Raman k=0

**P(********)**

**Time [ms]**

**Time [ms]**

- time

- time

- Ramsey

- Rabi

- /2

- /2

## S1/2

- 0

- 1

- 2

- S1/2

- |

- |

**•**
**•**
**•**

- Motion-sensitive Raman transitions:
- sideband cooling and phonon mediated entanglement .

- 0

- 1

- 2

**•**
**•**
**•**

- P3/2

- ion

- Raman beams

**Blue sideband (Anti-Stokes)**
**|********,n******** ******** |********,n-1******

**Red sideband (Stokes)**
**|********,n******** ******** |********,n+1******

## Laser-cooling Cd+ to n=0 

- Stokes
- |,n  |,n+1

- Anti-Stokes
- |,n  |,n-1

- |

- |

- |

- |

-   n
- 1+n

- IAS
- IS

- =

- xrms = 3 nm
- “Lamb-Dicke” regime

- Laser-cooling Cd+ to n=0
- (3.6 MHz trap)

- Thermometry:

**L. Deslauriers et al. quant-ph/0404142**

- Raman Cooling
- n < 0.05

- Doppler Cooling
- n  6

## Anomalous heating of trapped Cd+ ion

- 0

- 10

- 20

- 30

- 40

- 50

- 60

- 0.0

- 0.2

- 0.4

- 0.6

- 0.8

- 1.0

- 1.2

- n

- Delay (ms)
- [after cooling, before measurement]

- dn/dt = 0.02 quanta/ms

- Anomalous heating of trapped Cd+ ion

- Molybedenum Paul trap
- MHz

## Electric Field Noise between 3-6 MHz

- ~ 1/*d* 4

- Heating due to
- fluctuating patch potentials (?)

**L. Deslauriers et al. **
**quant-ph/0404142**
**PRA (in press)**

- See also
- Q. A. Turchette, et al.
- PRA **61**, 063418 (2000)

## Basic two-ion phase gate with a spin dependent force

- Basic two-ion phase gate with a spin dependent force

- |

- |

- p

- x

- Area

- Area

- laser

- Theory: Milburn-Schneider-James,
-               Molmer-Sorensen

- Benefits:
- -No individual addressing required.
- -High fidelity possible at finite temperature!

- SHO
- phase space

- [Expt: NIST Boulder Z (M-S-J) gate]

## Z -dependent force

- Z -dependent force

- A differential Stark shift permits a Z dipole force

- 1,1

- 0,0

**|********z******

**|********z******

- _Magnetic-field sensitive qubit_:
- Differential Stark shift easy!
- BUT poor qubit coherence

- _Field insensitive clock states_:
- Good qubit coherence
- BUT no differential Stark shift!(HF→

- 1,0

- 0,0

**|********z******

**|********z******

- Same coupling for
- arb. polarization!

- Stark shift

## Spin-dependent (X) force for a field insensitive qubit 

- Applied to two ions, this gives
- a Molmer-Sorensen entangling gate
- PRL 82, 1971 (1999)

## X force on a single ion 

- 0

- 1

- 2

- |z

- |z

**•**
**•**
**•**

- 0

- 1

- 2

**•**
**•**
**•**

- For **|********X******** or |********X******** **
- motion changes;
- spin superposition
- stays the same.

- Start in |Z =[|X+  |X] |motion=0
- | = |X[|] +  |X [|-]
-       = |Z[|  |] +  |Z [|+ |-]

- |X

- |X

- p

- x

- 

## Single ion x gate: generation of Schroedinger-Cat states: “cat scan”

- Single ion x gate: generation of Schroedinger-Cat states: “cat scan”

- “Molmer-Sorensen” detuning  (kHz)

- -30

- -20

- -10

- 0

- 10

- 20

- 30

- 0.0

- 0.1

- 0.2

- 0.3

- 0.4

- 0.5

- P(Z)

- c) =3kHz

- ...

- (a)

- (b)

**(c)**

- p

- x

- MS=500s
- n  6

- prep. |Z

- MS

## Fixing the optical phase sensitivity of  the “X” gate

- 

- Beatnote running waves
- in same direction...

- ... slow phase
-    fluctuation 
-    written on qubit

- 

- ... slow phase
-    fluctuation 
-    cancels

- Beatnote running waves
- in opposite direction...

- Fixing the optical phase sensitivity of  the “X” gate

- 

- Actually a
- -“phi” gate!!!

*********R ************B  ******→ ************MS ******= ***

*********R ********************B  ******→ ************MS************= 0***

- Red, blue sidebands

## Testing the phase sensitivity with one ion.

- prep. |Z

- MS

- 

- 

- 

- 

- (Actually
- echo used)

- MS

- Stable configuration
- MS – stable

- Unstable configuration
- MS – drifts

- P(Z)

- P(Z)

- deg

## Entanglement between a single atom and single photon:  towards photon mediated ion entanglement

- |

- |

**2****S****1/2**

**2****P****3/2**

- 

- 

-  108/sec

- ideal qubit memory:
- HF states in a single trapped ion

- ideal qubit transmitter:
- a single photon

- single trapped 111Cd+ atom

- excitation

- 

-  (m=0)

-  (m=1)

- see only 
- along this view

- | = || + ||
- (postselected)

## success probability per cycle

- PBS

- D1

- D2

- ion

- /2

- microwaves

- (- = H)

- (+ = V)

- excitation  beam

- spontaneous emission

-    Psucc 	= (Pexc)(coll)(det)
- 	= 10-4 now
- (Psucc ~ 0.2   possible with fast
- 	       laser and cavity)

- /4

## Verify entanglement: |ideal = ||V + ||H

- _Measured correlation:_
- |H | = 97%
- |H | = 3%
- |V | = 6%
- |V | = 94%

- Verify entanglement: |ideal = ||V + ||H

- Measured correlation after
- _rotating __**both**__ qubits by ____/2:_
- |H | = 89%
- |H | = 11%
- |V | = 6%
- |V | = 94%

- If mixed state,
- all probabilities
- would be 50%

- Observed Entanglement Fidelity F  87%

- Correlations in unrotated ...                and  rotated (π/2) basis.

- B.B. Blinov, D.L. Moehring, L.-M. Duan, and C.Monroe, *Nature *428, 153 (2004)

**atom qubit**

**photon qubit**

## D

- C. Cabrillo, et. al.,. *Phys. Rev. A* **59**, 1025 (1999)
- L.-M. Duan, et. al., *Phys. Rev. Lett.* **90**, 253601 (2003)
- C. Simon, et. al., *Phys. Rev. Lett*. **91**, 110405 (2003)

- ... and for _*scalable*_ quantum computing!

- L.-M. Duan, et. al., quant-ph/0401020 (2004)

- conventional entanglement
- (through motion) locally

- BS

- coincidence

## Quantum CCD	       Kielpinski, Monroe, Wineland, Nature (2002)

## Conclusions

- High fidelity qubit detection, ground state Raman cooling.
- Heating appears favourable for Cd system.
- Bichromatic X force for Schroedinger cat formation and ion gates with optical phase insensitivity.
- Single ion - single photon entanglement.
- Near Future:
- 1) Two ion entangling gates (Molmer-Sorensen).
- 2) Ion shuttling in “Tee” trap geometry
- 		      3) Teleportation using ion-photon entanglement
- 		      4) Demonstrate operation  of GaAs lithographic traps

- Cadmium system

## http://iontrap.physics.lsa.umich.edu/

- PI: Chris Monroe
- Jim Rabchuk (Visiting FOCUS Fellow,
- West. Illinois Univ.)
- PDs: Boris Blinov
-          Paul Haljan
-          Winfried Hensinger
- Grad students:
- Mark Acton
- Kathy-Anne Brickman
- Louis Deslauriers
- Patty Lee
- Jie Li
- Martin Madsen
- David Moehring
- Daniel Stick.
- Undergrads: David Hucul
- 	     Rudy Kohn Jr.
- 	     Jacob Sauer (REU)

- Former members: Russell Miller(undergrad), Chitra Rangan (U. Windsor)