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Quantum Chessboards in Ultrafast Optical Control of the Deuterium Molecular Ion

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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

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

Outline

The Concept

Features of the Chessboard

Observing the Chessboard Experimentally

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

5.0

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

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?

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!!

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)

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)

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

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

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.

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

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)

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.

An Explanation to the Population Transfer

D2+

2pσu

Potential

1sσg

Control @ τc

Pumpfrom D2

τc = 294 fs

τc = 308 fs

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

2/3 state mixes

τc = 46 fs

Initial FC

τc = 102 fs

e.g.Pop(ν= 4) = Pop(ν= 5) = 0.5

Single State Quenching

τc = 100 fs

τc = 130 fs

e.g. Pop(ν= 5) = 1.0

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)