1 Trey Porto Joint Quantum Institute NIST / University of Maryland Open quantum systems: Decoherence and Control ITAMP Nov Coherent Control of Atoms in a Double-Well Optical Lattice

Desire: Coherent Control Vibrational Control (external) Spin Control (internal) Our system: optically tapped cold neutral atoms

Desire: Coherent Control Vibrational Control Spin Control MergingMoving Auxiliary state control qubit state control

Control Testbed: 2D Double Well ‘ ’ ‘  ’ Two different period lattices with adjustable - intensities - positions += AB 2 control parameters

+ = /2 nodes  BEC Mirror Folded retro-reflection is phase stable Polarization Controlled 2-period Lattice Sebby-Strabley et al., PRA (2006)

Vibrational control of atoms in a double-well lattice Sub-lattice addressing (sub-wavelength optical MRI) Controlled spin-exchange 2-neutral atom interactions Testbed Demonstrations

Controlled 2-atom spin-exchange

Onsite exchange -> fast 140  s swap time ~700  s total manipulation time Population coherence preserved for >10 ms. ( despite 150  s T 2 *! ) Anderlini et al. Nature (2007)

Toward 2-qubit gate - Initial Mott state preparation (~30% holes) - Imperfect vibrational motion ~85% - Imperfect projection onto T 0, S ~95% - Sub-lattice spin control >95% - Field stability T 2 ~300  s Global exchange interaction current limitations:

Toward 2-qubit gate - Initial Mott state preparation (~30% holes) - Imperfect vibrational motion ~85% - Imperfect projection onto T 0, S ~95% - Sub-lattice spin control >95% - Field stability T 2 ~300  s Filtering/state preparation Coherent quantum control Move to clock states T 2 *= 60 ms, T 2 > 300ms Coherent Hyperfine control Global exchange interaction current limitations:

Outline I.Vibrational Control II.Spin Control

~0.5 ms transfer time fidelity limited by vibrational energy scale competes with spin-coherence times. mapped at t 0 from ‘ ’ lattice mapped at t f from ‘ /2’ lattice Adiabatic vibrational transfer

For the spin-exchange, we compromised: with vibrational fidelity F ~0.80 to 0.85 Improve spin-coherence and vibrational control

coherent quantum control techniques improve both speed and fidelity Coherent Quantum Control Step 1: reasonable model of the system Measured populations as a function of tilt during merge

Coherent Quantum Control Step 1: reasonable model of the system With G. De Chiara and T. Calarco Measured populations as a function of merge time

Optimized Control Step 2: optimize the control theoretically Gate control parameters Un-optimized left well projections Unwanted excitation unoptimized optimized Ask for 150  s optimization time With G. De Chiara and T. Calarco

Quantum control techniques unoptimized optimized Optimized at very short merge time and only for vibrational motion! (Longer times and full optimization should be better.) Step 2: optimize the control theoretically Gate control parameters With G. De Chiara and T. Calarco

Quantum control techniques unoptimized optimized Experimental consideration: band width of feedback Step 2: optimize the control theoretically Gate control parameters With G. De Chiara and T. Calarco

Quantum control techniques Step 3: Implement optimization

Outline I.Vibrational Control II.Spin Control

Sub-Wavelength Addressing State dependent light shift looks like local B-field Polarization modulation in an optical lattice Polarization modulation in a focused beam

Sub-lattice addressing in a double-well Make the lattice spin-dependent Apply RF resonant with local Zeeman shift OPTICAL MRI

Sub-lattice addressing in a double-well Left sites Right sites ≈ 1kGauss/cm ! Lee et al., PRL (2007)

optical 87 Rb Choices for qubit states Field sensitive states At high field, quadratic Zeeman isolates two of the F=1 states 1 m F = -2 m F = -1 Easily controlled with RF Optical MRI works

optical 87 Rb Choices for qubit states Field sensitive states At high field, quadratic Zeeman isolates two of the F=1 states 1 m F = -2 m F = -1 Easily controlled with RF Optical MRI works Problems: - field sensitive states = very bad qubit - Optical MRI field affects neighboring qubit states T * 2 = 120  s

optical 87 Rb Other Choices for qubit States Field insensitive states at B= m F = -2 m F = -1

optical 87 Rb Other Choices for qubit States m F = -2 m F = -1 Field insensitive states at B=3.2 Gauss

Clock States Improve coherence time by moving to clock states Switch to clock states: Field insensitive  wave control Optical MRI addressing does not directly work on clock states

Clock State Coherence T 2 ~ 300 ms (prev. 300  s) Improve coherence time by moving to clock states 3.2 Gauss

Clock State Coherence T * 2 ~ 20 ms (prev. 150  s) Improve coherence time by moving to clock states T * 2 ~ 60 ms (prev. 150  s) 3.2 Gauss Time (ms) Contrast

Optical Addressing of Clock States Need a technique to address clock states Transitions between clock states are MRI-addressable Develop techniques to addressably map qubit states Field sensitive transitions Field insensitive Field sensitive

Hyperfine Manifold Control Develop techniques for robust Hyperfine manifold control qubit mapping not entirely trivial - near degeneracies - quadratic shifts Theory input from I. Deutsch Symmetry breaking  wave Field insensitive Field sensitive

Example: single-site qubit addressing Memory qubits are distinct from “activated” qubits Goal: arbitrary qubit rotation on a single site Field & position insensitive

Example: single-site qubit addressing Goal: arbitrary qubit rotation on a single site qubit mapping is position sensitive Memory qubits are distinct from “activated” qubits

Example: single-site qubit addressing Goal: arbitrary qubit rotation on a single site Isolated qubit control Memory qubits are distinct from “activated” qubits

Example: single-site qubit addressing Goal: arbitrary qubit rotation on a single site Reverse process Memory qubits are distinct from “activated” qubits

Example: single-site qubit addressing Memory qubits are distinct from “activated” qubits Goal: arbitrary qubit rotation on a single site

Attractive approach: - field insensitive states = good qubit - No cross-talk Optical MRI field does not affect neighboring sites - Optical MRI mapping is a simple  -pulse: very amenable to robust pulse control “Activated” Qubit Mapping

Sub-Lattice Qubit Mapping Demonstrate these techniques in our double-well lattice

Mapped Ramsey Step 1: verify clean Ramsey fringe on clock Phase /  Open and close 2-pulse Ramsey sequence on Population

Mapped Ramsey Step 2: Ramsey fringe preserved with OMRI field -Open Ramsey on, -add left/right field gradient, -close Ramsey sequence on

Mapped Ramsey Step 2: Ramsey fringe preserved with OMRI field Phase Population Left Right Left sites Right sites -Open Ramsey on, -add left/right field gradient, -close Ramsey sequence on

Mapped Ramsey Step 2b: determine optical field strength Left sites Right sites

Mapped Ramsey Step 3: Map qubit on left, maintaining coherence -Open Ramsey on, -add left/right field gradient, map to, only on left -close Ramsey sequence right: left:

Mapped Ramsey Step 3: Map qubit on left, maintaining coherence Left sites Right sites -Open Ramsey on, -add left/right field gradient, map to, only on left -close Ramsey sequence right: left:

Mapped Ramsey Step 3: Map qubit on left, maintaining coherence Left sites Right sites -Open Ramsey on, -add left/right field gradient, map to, only on left -close Ramsey sequence right: left: Use quadratic Zeeman effect to avoid leakage

Mapped Ramsey Step 3: Map qubit on left, maintaining coherence -Open Ramsey on, -add left/right field gradient, map to, only on left -close Ramsey sequence right: left: LEFT RIGHT

Mapped Ramsey Sequence !! Step 3: Map qubit on left, maintaining coherence -Open Ramsey on, -add left/right field gradient, map to, only on left -close Ramsey sequence right: left: LEFT RIGHT

Mapped Ramsey Sequence !! Step 3: Map qubit on left, maintaining coherence -Open Ramsey on, -add left/right field gradient, map to, only on left -close Ramsey sequence right: left: LEFT RIGHT Should be improvable with robust (composite) pulse techniques

Example Composite Pulse Improvements  -pulse CORPSE pulse detuning insensitivity

Example Composite Pulse Improvements  -pulse CORPSE pulse detuning insensitivity Want arbitrary Unitary control + Insensitivity to errors

Future Direction Collaboration with Inst. d’Optique BEC production transport atom cloud Separate chamber Comercial aspheres

Postdocs John Obrecht Nathan Lundblad Double-well Team Patty Nathan John Former postdocs/students Bruno Laburthe Chad Fertig Jenni Sebby-Strabley Marco Anderlini Ben BrownPatty Lee Ken O’Hara Johnny Huckans

The End

+ - Symmetrized, merged two qubit states interaction energy

+ - Symmetrized, merged two qubit states Spin-triplet, Space-symmetric Spin-singlet, Space-Antisymmetric

Lattice Brillioun Zone Mapping

Example: Addressable One-qubit gates  Optical Magnetic Resonance Imaging

Example: Addressable One-qubit gates Optical Magnetic Resonance Imaging

Example: Addressable One-qubit gates RF,  wave or Raman Optical Magnetic Resonance Imaging

Example: Addressable One-qubit gates Zhang, Rolston Das Sarma, PRA, (2006) Optical Magnetic Resonance Imaging