Download The Need for an Open Quantum System Approach to Describe High

The Need for an
Open Quantum System Approach to Describe
High-Intensity X-ray Interactions with Matter
August 3rd, 2010
Nina Rohringer
(Lawrence Livermore National Laboratory)
This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
LLNL‐PRES‐448504
Lawrence Livermore National Laboratory
Non-linear optical physics in the X-ray regime
Linear effects (one-photon one-electron interactions):
• Coherent diffractive imaging
• Time-resolved photo-absorption spectroscopy (RIXS, XANES)
• Time-resolved photoelectron spectroscopy • Spectroscopy of highly-charged ions (EBIT)
Quantum optics transferred to the X-ray regime
Atomic x-ray lasing with innershell transitions
Rabi Flopping 3p
3p
2p
2s
2p
2s
0.5 fs
3 fs
1s
Rohringer and London, Phys. Rev. A (2010)
Option:UCRL#
Resonant Raman Scattering
1s
Rohringer and Santra, Phys. Rev. A (2008).
Option:Directorate/Department Additional Information
2
Non-resonant versus resonant high-intensity x-ray matter interaction
Resonant Auger-electron spectrum
L. Young et al., Nature 466, 56 (2010) Rohringer and Santra,
Phys. Rev. A (2008)
Non-resonant interaction
 
 
1st user experiment at LCLS on Neon
Sequence of one-photon absorption events
followed by Auger or radiative decay
  Model of kinetic rate equations valid
Option:UCRL#
Resonant interaction  
 
 
 
Increased coupling strength on resonance
Perturbation theory breaks down
Non-linear description necessary
Optical Bloch equations for a dissipative system
Option:Directorate/Department Additional Information
3
Occupation of a specific chargestate / Inensity [arb. unit.]
Focusing LCLS into a gas sample of Neon
Parameters: pulse of 100 fs, 1012 photons, ω=1.4 keV, focused to 2 µm
Option:UCRL#
Time [fs]
Rohringer and Santra, Phys. Rev. A, (2008).
Option:Directorate/Department Additional Information
4
An atomic inner-shell X-ray laser pumped with XFEL radiation
based on Neon
2p
2s
2 fs
XFEL pump
at 1 keV
1s
2p
2s
1s
Inner-core
photo-ionization
Auger decay
160 fs
XFEL pump
at 1 keV
2p
2s
2p
2s
Lasing transition
@ 850 eV
1s
Spontaneous emission
1s
Inner-core
photo-ionization
Experimental scheme:
Atomic gas volume
Focused
XFEL beam
Option:UCRL#
Atomic x-ray laser
(amplified spontaneous emission)
Option:Directorate/Department Additional Information
5
Small-gain parameters at 1 keV pumping energy
I(z,t) = I(0,t) ⋅ e g⋅n⋅z
(single atom calculcation)
Δω /ω = 3⋅10 −4
Ne 1+
Ne 1+
2p
2p 2s
2s
Ne 2+
Ne 2+
2p
2p
2s
2s
Ne 3+
Ne 4+
2p2p
2s2s
Electron–ion collision times:
at 100 eV (slow photoelectrons) ≈ 800 fs
1s
1s 1s
1s
(for density of 1019 cm-3) at 800 eV1s(fast Auger
1selectrons) ≈ 570 fs Auger decay Double Auger decay
ions are at room temperature !
6
Option:UCRL#
Option:Directorate/Department Additional Information
One-dimensional self-consistent gain calculation
Upper lasing level:
X-ray laser flux in forward and backward direction:
Atomic x-ray laser
Atomic gas volume
Focused
LCLS beam
j(z,t)
(amplified spontaneous emission)
jXRL(z,t)
2 μm
z=L
z=0
5 mm
Expected output of atomic inner-shell x-ray laser
9x109 photons in XRL line
Intensity: 7x1016 W/cm2
Duration: 0.5 fs
0.5
fs
0.75 fs
n=4x1018 cm-3, LCLS: 100 fs, 1012 photons per pulse, focal diameter 2 μm
Saturation of more than one lasing line seems possible
Rohringer and London,
Phys. Rev. A (2009).
XFEL: 2 µm focus, 5x1012 photons per pulse, 100 fs pulse, 1keV energy
gas density: 1x1019 atoms/cm3
Option:UCRL#
Option:Directorate/Department Additional Information
9
Gain cross section
Number of photons
2p
2s
2p
2s
Exponential
gain regime
2p
2s
1s
1s
2
2+: 1s 2s22p4
1s
At saturation
2p
2s
1s
1+: 1s22s22p5
2+:
2p
2s
1s
3+: 1s12s22p4
2p
2s
2p
2s
1s
1s
1s12s22p5
Output at end of amplifying plasma column for 1 keV pump
Pathway to multi-color x-ray fs pump-probe experiments
E
#(photons)
Ipeak
850 eV 3x1010
7x1016 W/cm2
862 eV 4x109
1x1016W/cm2
855 eV 6x107
5x1014W/cm2
To determine spectrum, coherence properties, propagation effects, refraction, etc.
-> Solve coupled Maxwell-Bloch equations Option:UCRL#
Option:Directorate/Department Additional Information
11
Scheduled experiment of XRL lasing scheme in Sept. 2010
Photo-ionization pumping scheme at different wavelengths
Beam
waist: ≈1 mm
aperture
slit
≈2 μm
focused LCLS beam
(divergence 1 mrad)
XRL beam
(divergence 0.5 mrad)
Gas cell filled
with neon (1 atm.)
≈1 m
LCLS beam
focusing
chamber
Hutch 1 (AMO)
Option:UCRL#
AMO high-field
chamber
CCD
grating
Chamber for
spectrometer
Hutch 2 (SXR)
Option:Directorate/Department Additional Information
12
Non-linear optical physics in the X-ray regime
Atomic x-ray lasing with
inner-shell transitions
Resonant Raman Scattering
Rabi Flopping 3p
3p
2p
2s
2p
2s
3 fs
1s
1s
0.5
fs
Option:UCRL#
Rohringer and Santra, Phys. Rev. A (2008).
2p
2s
2p
2s
1s
1s
Option:Directorate/Department Additional Information
13
Resonant Auger effect at high X-ray intensities, Ne 1s-3p transition,
Wave-function approach
Coupling strength
(Rabi frequency)
3p
3p
2p
2s
2p
2s
Ω(t) = E(t) ⋅ 3p z 1s
3p z 1s ≈ 0.01 a.u.
3 fs
1s
1s
Rohringer and Santra, Phys. Rev. A (2008)
Option:UCRL#
Option:Directorate/Department Additional Information
14
Resonant Auger-electron spectrum gets broadened
Coherent Gaussian Pulse
Single SASE
pulse
Single
SASE pulse
Ensemble Average
averageover ensemble of pulses
Rohringer
Option:UCRL# and Santra, Phys. Rev. A (2008)
Option:Directorate/Department Additional Information
15
Generalized Bloch equations for open quantum system
Calculate time-dependent ionic density matrix
Valence Ionization
Auger
Decay
Resonant
Coupling
2p
2s
2p
2s
2p
2s
2p
2s
1s
1s
1s
or
1s
Loss of coherence,
Open Quantum System,
Unobserved photo electrons
⎡ −iδt R* (t)
⎤
ρ˙11 = ⎢ie ρ21
+ cc ⎥ + σ 1 j(t) p0 (t)
2
⎣
⎦
R(t)
⎡
⎤
ρ˙ 22 = −Γ2 ρ22 + ⎢ie iδt ρ12
+ cc ⎥
2
⎣
⎦
Γ2
R* (t)
−iδt
ρ˙12 = − ρ12 + ie ( ρ22 − ρ11 )
2
2
Rohringer and Santra, work in progress
Option:UCRL#
Option:Directorate/Department Additional Information
16
Self-Stimulated Resonant Raman Scattering
Atomic x-ray lasing with
inner-shell transitions
Resonant Raman Scattering
Rabi Flopping 3p
3p
2p
2s
2p
2s
3 fs
1s
1s
0.5
fs
Option:UCRL#
Option:Directorate/Department Additional Information
17
Proposed experiment: Resonant pumping scheme
3p
2p
2s
K-edge:
1140eV
LCLS pump
@ 1174 eV
2p
2s
2p
2s
….…
1s
1s
Inner-core
Auger decay
Photo-ionization
Ne 1+
Ne 2+
Strong non-linear coupling !!
2p
2s
1174 eV
1s
Li-Ne 7+
2p
2s
1018 eV
3p
2p
2s
3p
1s
Resonant
excitation
He-like Ne 8+
Time
1s
1072 eV
1s
Pathway will depend
On x-ray intensity !
Comparable oscillator strengths!
3p
174 eV
2p
2s
2p
2s
1008 eV
1s
1s
Self-stimulated resonant Raman scattering
Option:UCRL#
Option:Directorate/Department Additional Information
18
Proposal: Stochastic wave function approach
Adopt stochastic wave-function approach from quantum optics
Ionic reduced density matrix sampled by ensemble of pure states
Ionic wave function evolves deterministic (resonant interaction with XFEL)
+ random (stochastic) quantum jumps to simulate -photo ionization processes
-Auger decay
-eventually treat electron impact ionization, excitation, de-phasing
Quantum jump approach:
Jump operators: derived by semiclassical approximation ?
Test on single-atom case
by comparing to generalized optical Bloch equations
(equivalent descriptions of determining ionic reduced density matrix)
dense gas volume/ clusters
Focused
XFEL beam
Option:UCRL#
Scattered x-ray
light
Option:Directorate/Department Additional Information
19
Acknowledgements
LLNL: Richard London
James Dunn
Felicie Albert Sebastien Le Pape
Alexander Graf CSU: Jorge Rocca
Duncan Ryan
Mike Purvis
SLAC: John Bozek
Christoph Bostedt
CFEL: Robin Santra
We acknowledge support of this project by
LLNLʼs LDRD (Laboratory Directed Research and Development) program.
Option:UCRL#
Option:Directorate/Department Additional Information
20