Quantum Chessboards in Ultrafast Optical Control of the Deuterium Molecular Ion

1. Quantum Chessboards in Ultrafast Optical Control of the Deuterium Molecular Ion Raymond King C R Calvert,T Birkeland, D S Murphy, J D Alexander, J F McCann, I D Williams G R A J Nemeth, W A Bryan W R Newell E L Springate, I C E Turcu, J Collier

2. Ultrafast Optical Control of the Deuterium Molecular Ion • State-selective control of D2+ vibrations • Sub-vibrational timescales (< 25fs) • Quantum encoding / information applications Ultrashort Laser Pulses Requirements –Pump, Control and Probe pulses ≤ 12 fs ( 1 femtosec = 10-15 sec ) Dissociation Deuterium molecule D2+ vibrations (20 - 35 fs) Modified motion

3. Outline The Concept Features of the Chessboard Observing the Chessboard Experimentally

4. Potential D2+ 2pσu 1sσg D2 Coherent superposition of vibrational states φv , each with associated frequency ωvand energy Ev = hωv Internuclear Separation (R) Creation of D2+ Vibrational Wavepacket D2+ 2pσu Potential Tunnel ionisation – Initiates a dynamic wavepacket in D2+ : 1sσg Time φ2 φ1 φ0 Pump Pumpfrom D2 Internuclear Separation (R) In our simulations we use populations, |av|2, given by the Franck-Condon distribution

5. 5.0 4.0 3.0 FFT Yield 0 200 400 600 Probe delay time, τp(fs) Observation of the wavepacket D2+ Using a Probe pulse we are able to induce photodissociation of the molecule. This effectively samples the wavepacket population at large R. 2pσu Potential 1sσg Probe @ τp D+ + D Ion yield has an oscillatory structure that reflects the motion of bound wavepacket. FFT analysis determines the vibrational beats contributing to wavepacket motion Pumpfrom D2 Internuclear Separation (R) Vibrational Beats

6. Controlling the Wavepacket D2+ Control Pulse Parameters – Intensity : 5 ×1013 – 2 ×1014 Wcm-2 Duration : 5 – 12 fs Polarisation – Parallel to molecular axis 2pσu Potential 1sσg Control @ τc Example: 5 × 1013 Wcm-2 Control pulse @ τc = 40 fs Pumpfrom D2 Internuclear Separation (R) But how does this affect the wavepacket motion?

7. Time Evolution of a Controlled Wavepacket No Control Pulse: <R> ≈ 2.5 a.u Control pulse @ τc = 40 fs: 50% dissociation Vibrationally cooled <R> ≈ 2 a.u Now lets look at these distributions for a range of control pulse delays!!

8. Absolute Population The Chessboard • Simulated 5 fs, 5 ×1013 Wcm-2 control pulse interactions • Delay range of 0 → 700 fs (i.e. up to the quantum revival)

9. Observed Vibrational Distributions By tuning the precise timing, duration and Intensity of the control pulse specific vibrational distributions can be optimised: • Uses • Possible quantum computing applications • Murphy et. al.New J. of Phys. (2007) e.g.2 State mix I0 = 1 × 1014 W cm-2 τc= 49.75 e.g. Single State I0 = 1 × 1014 W cm-2 τc= 51.25 • Imaging R-dependent nodal structure of single vibrational states • Niederhausen et. al. Phys. Rev. A (2008)

10. 308 Absolute Population The Centrepiece of the ChessboardEven or Odd Superpositions 2pσu τc = 294 fs τc = 308 fs 1sσg Control @ 294 fs EVEN ODD Δν = ± 1

11. How do we Observe this Experimentally? Using the Previous technique of probe induced photodissocation  A 5 fs 4 ×1014 Wcm-2 probe pulse interaction was simulated over a range of delays τp → 4000 fs, in 1 fs steps. An FFT was then carried out on the simulated PD ion yield. Second order beats (i.e. ων→ ων+2) observed to only have amplitudes for either odd or even ν depending on the timing of the control pulse. EVEN ODD

12. Experimental Advantages to the Centrepiece Numerous simulations were carried out to characterise the odds/evens effect in the chessboard: Flexibility in Pulse Duration: Works for control pulse durations of 5 → 12 fs Flexibility in initial vibrational distribution: Occurs as long as a range of vibrational states are excited coherently from the pump process. (FC not strictly necessary) Flexibility in Control delay, τc: Odd/evens effect should be seen for τc within ± 1 fs.

13. Summary • We have simulated control pulse conditions and possible outcomes - 2 or 3 State Superposition - Single State Enhancement - Odds/Evens Superposition • Odds/evens distribution shows flexibility in experimental parameters • Proposed method for observing odds/evens effect experimentally

14. Merry Christmas and Happy New Year ! From UltrafastBelfast.co.uk Vibrational Control of D2+ - D S Murphy et al. :New J. Phys. 9 260 (2007) Quantum Chessboards in the Deuterium Molecular ion - C R Calvert et al. : J. Phys. B 41 205504 (2008) Controlling Dissociationin the Deuterium Molecular ion - D S Murphy et al. : JPB, 40, S359 – S372 (2007) Vibrational Revivals in D2+ - W A Bryan et al. : Phys. Rev. A 76, 053402 (2007)

17. Experimental Advantages to the Centrepiece Numerous simulations were carried out to characterise the odds/evens effect in the chessboard: Pulse Duration: Effect observed for pulse durations of 5 → 12 fs Initial vibrational distribution: As long as a range of vibrational states are excited coherently from the pump process the effect is still observed (FC not strictly necessary). Control delay, τc: Unlike other controlled distributions the odd/evens effect is not as dependent on the specific control pulse delay and has a freedom of ± 1 fs.

18. An Explanation to the Population Transfer D2+ 2pσu Potential 1sσg Control @ τc Pumpfrom D2 τc = 294 fs τc = 308 fs

20. D2+ 2pσu Potential 1sσg Control @ τc φ2 φ1 φ0 Pumpfrom D2 Internuclear Separation (R) The Experiment Tunnel ionisation – Initiates a dynamic wavepacket in D2+ : Coherent superposition of vibrational states φv , each with associated frequency ωv

21. 2/3 state mixes τc = 46 fs Initial FC τc = 102 fs e.g.Pop(ν= 4) = Pop(ν= 5) = 0.5

22. Single State Quenching τc = 100 fs τc = 130 fs e.g. Pop(ν= 5) = 1.0

25. Merry Christmas and Happy New Year ! From UltrafastBelfast.co.uk Vibrational Control of D2+ - D S Murphy et al :New J. Phys. 9 260 (2007) Quantum Chessboards in the Deuterium Molecular ion - C R Calvert et al : J. Phys. B 41 205504 (2008) Controlling Dissociationin the Deuterium Molecular ion - D S Murphy et al : JPB, 40, S359 – S372 (2007) Vibrational Revivals in D2+ - W A Bryan et al : Phys. Rev. A 76, 053402 (2007)