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Controlling the future – lessons from Quantum Mechanics
“Prediction is a difficult thing – especially of the future” - Nils Bohr
Controlling the future – lessons from Quantum Mechanics
“All is foreseen but permission is granted” – The Talmud
“Prediction is a difficult thing – especially of the future” - Nils Bohr
Controlling the future – lessons from Quantum Mechanics
“All is foreseen but permission is granted” – The Talmud
Is the future determined?
If yes, can we predict it?
If yes, can we control it?
“Prediction is a difficult thing – especially of the future” - Nils Bohr
Newtonian Mechanics:
Given the position and velocity of a macroscopic body in the present we can use Newton’s second law
F=ma where F is the force acting on the body, m is it its mass, and a is the acceleration, to calculate the position and velocity of that body at any time t in the future. This can in principle be repeated for each and every particle in the universe, so seemingly, not only is the future determined by the state of the universe in the present but we ought to be able to predict where it is going by solving Newton’s second law equation.
t (future)present
In practice we can only calculate the trajectories of simple systems (e.g., a planet orbiting the sun) over sufficiently long times. When more bodies are involved, in most cases the motion becomes “chaotic”. When chaos occurs it is impossible to solve Newton’s equations of motion to sufficient accuracy: the further in the future we inquire, the better do we need to know the present positions and velocities of all bodies involved. The degree of accuracy of our knowledge of the present must increase exponentially, the further in time we desire to predict the future.
sun
earth
An example: Set N billiard balls along a straight lineand try to hit the first billiard ballsuch that the last one is pocketed.This becomes exponentially more difficultwith N.
Quantum Mechanics:
Quantum Mechanics describes the motion of microscopic bodies
(e.g., an electron, a photon, an atom, a molecule). The equations of
motion are those of waves (“wave functions”). These equations do
not give rise to chaotic behavior: Given the wave function in the
present we can calculate its value at any time in the future to
sufficient accuracy even when a large number (hundreds) of
microscopic bodies are involved.
Does that mean that Quantum Mechanics allows us to predict
the future?
Not necessarily. The wave function tells us about the whereabouts
of the particle only in a statistical way: It tells us what we are likely
to observe, i.e., what is the distribution of outcomes when we
repeat the same experiment many many times.
ph
ase (=an
gle)
0o
Waves and phases
Projection on a line
Circular motion
0o
amplitude (=length of projection)
angle=
ph
ase
ph
ase
ph
ase
ph
ase
ph
ase
ph
ase
ph
ase
180o
180o
0o
ph
ase
180o
0o
ph
ase
180o
0o
ph
ase
180o
0o
ph
ase
180o
0o
ph
ase
180o
0o
ph
ase
180o
0o
ph
ase
180o
0o
ph
ase
180o
0o
ph
ase
360o
360o
180o
0o
ph
ase
360o
360o
+
-
amplitude
phase
+
-
phase
wave function 2probability =
probability
wave function
phase
+
+
-
wave function at present (t=0) wave function in the future (t=1 ps)
given the we can calculate the
Interference between waves going through two slits
+
+
+
+
-
-
-
-
a
b
+
+
+
-
-
+
+
+
+
-
-
-
-
0
0
Screen
a
b
“destructive”
“constructive”
“destructive”
Probability
+
+
+
+
-
-
-
-
0
0
Screen
a
b
+
+
+
+
-
-
-
-
0
0
P = (a+b)2 = a2 + b2 + 2ab
If a=b then P=4a2
If a= - b then P=0
P=
4a2
a
b
P=
0
+
+
+
+
-
-
-
-
0
0
a
b
But this interference pattern is never seen in any individual event!
+
+
+
+
-
-
-
-
0
0
a
b
+
+
+
+
-
-
-
-
0
0
a
b
+
+
+
+
-
-
-
-
0
0
a
b
+
+
+
+
-
-
-
-
0
0
a
b
+
+
+
+
-
-
-
-
0
0
a
b
+
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+
-
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-
0
0
a
b
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+
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+
-
-
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-
0
0
a
b
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+
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+
-
-
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0
0
a
b
+
+
+
+
-
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-
-
0
0
a
b
P
robability
+
+
+
+
-
-
-
-
0
0
Screen
a
b
How then can we control the outcome of microscopic events. e.g. chemical reactions?
Or in greater generality:
H-O + D H D H + O-DO
Cleave the O-D bond Cleave the O-H bond
BA-B + C A C A + B-C
Cleave the B-C bond Cleave the A-B bond
where A, B, or C can be any atom or any group of atoms.
matter wave (particle)
let a
matter wave (particle)
light wave
let a
interact with a
matter wave
light wave
amplitude for theparticle to absorbthe light waveand be excited
“Entangling” light and matter waves
light wave a
light wave a
matter wave
light wave a
amplitude forabsorbinglight wave a
light wave a
light wave b
phaseshift
amplitude forabsorbinglight wave a
light wave a
light wave b
phaseshift
amplitude forabsorbinglight wave a
amplitude forabsorbinglight wave b
light wave a
light wave b
phaseshift
amplitude forabsorbinglight wave a
matter wave after absorptionof light wave b
interfere
A-B + C
A + B-Cthe “screen” ofphases
The key to control is that the interference patterns of different outcomesbe shifted in phase.
- is favored
A-B + C
A + B-C
- is favored
A-B + C
A + B-C
- is favored
A-B + C
A + B-C
- is favored
How does it work in real experiments?
Control of the direction of electronic motion: current without voltage!
“slit” a “slit” b
- +
Distance from origin proportional to magnitude at a given direction
Polar plots: a way of plotting angular distributions
- ++
1- photon absorption
+2- photon absorption
+
-++
-
Symmetric
Symmetric
Anti-symmetric
or
- +
+
+
+-
+-
- +
+
+- +
+
-
- +
E. Dupont, P.B. Corkum, H.C. Liu, M. Buchanan, and Z.R. Wasilewski, Phys. Rev. Lett. 74, 3596 (1995)
forward
backward
0 / 2
2 2
2(( ) ,
2)
iH
dH
m dV U x tx
x
2( / )
0 |x|>0.1 nm( )
-0.5 eV |x|<0.1 n
( , ) sin sin 2 (
m
)
( ) t
U x t x t t f t
t
x
f
V
e
-200 -100 0 100 200
-0.5
-0.4
-0.3
-0.2
-0.1
0
x [A]
V(x
) [eV
]
=0.1; t= 3 10-2 [au]=150 nstep=100; N
T=2000;
(x,t=0)=0(x)
+
+
+
+
-
-
--
0
0
a
b
We have thus been able to transform a probabilistic situation to a situation of certainty. This is exactly what happens when we make a measurement, the wave function with its associated probability “collapses” to a single value which is the “spot” that we see.The main difference is that in a measurement we cannot control where the “spot” appears.
“spot”
This sheds new light on the very act of measurement: instead of entanglingthe particle wave with the light wave, the particle to be measured getsentangled with the atoms of the measuring device. It undergoes a similarmulti-path interference, whose nature changes constantly and rapidly with time. The particle gets absorbed by a detector atom when its wave function assumes the value of 1 at the position of a given detector atom.
• 1986: Original suggestion to use quantum interference for control. Introduction of the concept “coherent control”.
Milestones in the development of “coherent control” blue – theory red - experiments
B + A-C A + B-C
12
E1
E2
E
Eg
4 3
1989: (with Kurizki) Introduction of 1 photon vs. 2 photon as a means of symmetry breaking and differential control: prediction of creation of DC photo current in semi conductors with no bias voltage.
ABC
A+BCB+AC
1988: (with Hepburn) Introduction of 1 photon vs. 3 photon interference as a means of control
backwarde-
forward
conduction band
1990: First experimental verification of the 1 vs. 2 coherent
control scenario. Control over photo-current directionality in
semiconductors (Zeldovitch)
1990/1991: First experimental verifications of the 1 vs. 3
coherent control scenario: The control of photoionization yields
in atoms (Elliott, Bucksbaum) and molecules (Gordon, Bersohn) 1991: Coherent control of molecular chirality
introduced
1994/1995: Interference Control with Incoherent light introduced
1995: Experimental demonstration of coherent control of photo-current generation in quantum wells by the 1 vs. 2 photon scenario (Corkum)
A+BCB+AC
1
-2 2
1995: Experimental demonstration of control of electronic hopping in a dissociating molecule, in 1 vs. 2 photon H+ + D HD+ H + D+ (DiMauro)
1995: (Gordon) First experimental demonstration of control over a branching process: control over the ionization vs. dissociation in 1 vs. 3 photon HI+ HI H + I
1996: First experimental demonstration of control over electronic branching ratios: interference control with incoherent light in Na + Na(3p) Na2 Na + Na(3d) (Shnitman+Yogev+,Shapiro)
1997: (with Vardi) Photoassociation of ultracold atoms to form ultracold molecules via Coherent Raman Process suggested
1997: First experiments on automated feedback control via pulse shapings (Wilson, Silberberg, Gerber)
1998: Experimental demonstration of coherent control via phase modulation of two photon absorption of atoms (Silberberg)
1998: (Gerber) First experimental demonstration of adaptive feedback control of a branching photochemical reaction: Control over the photodissociation of Fe(CO)5 and
Cp + 2CO +FeCl CpFe(CO)2Cl CpFeCOCl + CO
2000: Coherent Control of refractive indices introduced
2000: (with Frishman) Enantiomeric purification of chiral
racemic mixtures by coherent control techniques
• 2000: Theory of nanoscale deposition on surfaces
• 2000: (with Frishman) Coherent Suppression of spontaneous emission using overlapping resonances
2001: Adaptive feedback control of the photodissociation of C6H5CO + CH3 C6H5CH3CO C6H5 + CH3CO in the high field regime (Levis)
2002: (with Kral): An exact analytical solution of the non-degenerate quantum control problem
2002: Adaptive feedback control of internal conversion channel in a light harvesting antenna complex of photosynthetic purple bacterium (Motzkus)
2003: (with Kral and Thanopoulos): An analytic solution for the degenerate quantum control problem
2003: (with Zhang and Keil) Experimental demonstration of phase locking between two 2-photon processes in 2-photon vs. 2-photon coherent control
2003-2004: Experimental control of high harmonic generation (Murnane, Gerber)
|2›|3›
|1›
|0›
|1’›|2’›
2004: Coherent Control techniques used in the “streak camera” phase measurement attosecond pulses (Krausz, Corkum)
• 2005: Control of radiationless transitions by interference between overlapping resonances
2005: (with Thanopoulos) Automatic repair of mutations caused by dihydrogenic tunneling between two nucleotides using coherent control
2005: (with Kral) Coherent control with non-classical light
2005: Experimental demonstration of coherent photoassociation of Rb + Rb BEC to form Rb2 molecular BEC using the Vardi+Shapiro scheme (Grimm)
2005: Experimental demonstration of bond breaking selectivity in the CH2=CH. + Cl CH2=CHCl CH= CH + HCl (Gordon)
2005: (with Segal) Suggestion of quantum computation using electron trapped in an
quadrupoles of carbon nanotubes
+E
-E
e
e
J
Barge Vishal J., Zhan Hu, and Robert J. Gordon, J. Chem. Phys. - submitted
Control of chirality: The importance of the “envelope phase”
The D S2 2 chiral isomers
The purification of a mixture of molecules with opposite handedness by optical means (Phys. Rev. Lett. 84, 1669 (2000)
A. Vardi, D. Abrashkevitch, E. Frishman, and M. Shapiro, J. Chem. Phys. 107, 6166 (1997)
1 2
Coherent Raman photoassociation of Rb+Rb Rb2
K. Winkler, G. Thalhammer, M. Theis, H. Ritsch, R. Grim, and J. Hecker Denschlag,Cond-mat/0505732 v1 30 May 2005
“Loop” adiabatic passage in chiral molecules
The D S2 2 chiral isomers
Symmetry breaking in loop systems
In the loop system the eigenvalues depend on the phases
The dependence of the population transfer on the phase
Detection and automatic repair of mutations by coherent light
Dihydrogenic tunneling in a dinucleotide pair
I. Thanopoulos and M. Shapiro, J.A.C.S. – in press
Tubular image states (TIS)
B. E. Granger, P. Král, H. R. Sadeghpour and M. Shapiro, PRL 89, 135506 (2002).
Suspended linear molecular conductors or dielectrics support highly-extended electronic states.
The electron is attracted to the material surface by its image charge and repelled by a centrifugal force due to its rotational motion.
The combination of these two effects yields effective potential curves having long range (10-50 nm) potential wells that support bound states that are separated from the surface, and can have long lifetimes at low temperatures.
The origin of attraction of TIS
2
2
-1/ 4( ) ( )
2eff
lV V
m
The stability of TIS is due to interplay between the attractive image potential and repulsive centrifugal potentials
Close to the surface the centrifugal potential and Coulomb attraction give rise to 1-2eV barriers
The total wave functions and eigenenergies:
, , ,
2 2
, , ,
1( , , ) ( ) ( )
2
2
iln l k n l k
n l k n l
z e z
kE E
m
Attractive part of the potential
Total potential at z=0
N=2-8
N=2 N=8
Detached local minimum
Potential Energy for Finite Segmented Systems
Optically induced electron transfer over barriers
e
Hopping of electrons over potential barriers with no net absorption of photons by implementing the Laser catalysis scenario.
A. Vardi, M. Shapiro, Phys. Rev. A 58, 1352 (1998).
Switch!Switch!Switch!Switch!
B. E. Granger, D. Segal, H. R. Sadeghpour,
P. Král and M. Shapiro, PRL, 94, 016402 (2005)
• We have studied TIS above nanotube arrays• The states can remain largely detached and form bands.
Image states bands over suspended arrays of nanowires
Z.P. Huang et. al. App. Phys. Lett. 82, 460 (2003)
Coherent Control as a Disentanglement Transformation
+
TheoryIoannis Thanopulos (Univ. of British Columbia) Einat Frishman (Univ. of British Columbia) Petr Kral (Univ. Illinois at Chicago) Dvira Segal (Weizmann )
Paul Brumer (University of Toronto) John Hepburn (University of British Columbia) Ilya Averbukh (Weizmann)
Experiment
Qun Zhang (Weizmann, now at Univ. of British Columbia) Alexander Shnitman (Weizmann) , Mark Keil (BGU)
Acknowledgments
