1. EXPLORING NATURE WITH A QUANTUM SIMULATOR
Kwek Leong Chuan,
Center for Quantum Technologies, National University of Singapore
Institute of Advanced Studies, Nanyang Technological University
Collaborators
Huo Mingxia,
Dimitris G. Angelakis,
Elica Kyoseva
Simons Conference on New Trends in Quantum Computation, 18 Nov 2010

2. He (the statistician) showed a reprint to his former classmate…
There is a story about two friends, who were classmates in high school, talking about their jobs.
One of them became a statistician and was working on population trends…..
He (the statistician) showed a reprint to his former classmate…
Disclaimer:
This story is meant for educational purposes only.
Any resemblance to real persons, living or dead, is purely coincidental.
Also…it is not politically correct!!!
12 May 2009

3. The Gaul distribution? Asterix?
Let me show you a reprint on the Gaussian distribution…
Pictures stolen from various “dubious” sources :
12 May 2009

4. So what are those symbols…..
12 May 2009

5. The ratio of the circumference of the circle to its diameter
Pie???
Is it edible?
Oh…
this is pi…
What is that?
Well, now you are pushing your joke too far…surely the population has nothing to do with the circumference of the circle
The ratio of the circumference of the circle to its diameter
12 May 2009

6. What are you working on this days now?
There are many processes in Nature that are described by equations that cannot be solved by ordinary computers…
Oh, I am trying to mimic physical processes in Nature with a quantum simulator!
So by building a quantum simulator experimentally, one could in principle solve computationally difficult physical processes through observation of laboratory processes that mimic the physical processes….
What is that?
What are you working on this days now?
Pictures stolen from various “dubious” sources :
19 April 2010
Talk Presented at KIAS

7. So what can you do with quantum simulator
So what can you do with quantum simulator? Can you do experiment with them like what I did in Iraq?
19 April 2010
Talk Presented at KIAS

8. Common Equations Basic Idea behind simulation….of any kind
Simulating system
Physical System
Common Equations

9. “Nature isn't classical, dammit, and if you want to make a simulation of Nature, you'd better make it quantum mechanical, and by golly it's a wonderful problem, because it doesn't look so easy.”

10. Universal Quantum Simulator
The rule of simulation that I would like to have is that the number of computer elements required to simulate a large physical system is only to be proportional to the space-time volume of the physical system. I don’t want to have an explosion!!
R. P. Feynman
I would like to have an exact simulation, in other words, that the computer will do “exactly” the same as nature
R. P. Feynman

13. Dimitris G. Angelakis et al, Phys. Rev. A 2007
See also New Scientist, 2007; Innovation 2010
M. J. Hartmann et al Nat. Phys. 2006; Andrew D. Greentree et al, Nat. Phys.2006

14.
Elmar Haller, et al. Nature, 2010

15. Luttinger liquid theory
One dimensional
electronic gas
Luttinger liquid theory
Collective excitations:
Spin excitations
Charge excitations
Different velocities for spin and charge: spin-charge separation
Recent efforts for measurement are inconclusive
We will simulate spin-charge separation in quantum optical systems

16. The physics of Lieb-Liniger model (bosonic atoms):
Realized in 1D optical lattices (experiments by Bloch et al.)

17. Two-component Lieb-Liniger model:
where the density
PRL 95, (2005)
Charge density:
PRA 77, (2008)
Spin density:

18. Strongly correlated effects with photons and polaritons
DGA, M. Santos, S. Bose, “Photon blockade induced Mott transitions and XY spin models in coupled cavity arrays”, (arXiv: June 06) Phys. Rev. A (Rap. Com.) vol. 76, (2007).
M. Hartmann, F. Brandao, M. Plenio, “Strongly interacting polaritons” (arXiv: June 06 ), Nat. Phys. 2, 849 (06);
Greentree et al, arXiv:cond-mat/ Quantum Phase transition of light, (arXiv: Sept 06, Nat. Phys. 2006)

19. Nature 424, 847 (2003)
PRL 94, (2005)
PRL 102, (2009)

20. Dark state polaritons in Electromagnetic Induced Transparency (EIT)
Experiments have shown that the pulse can be slowed down and eventually stored in atomic excitations.
dark state polariton:
dark states
Group velocity:

21. Storing light in atoms through EIT
switch off adiabatically
atomic excitation
switch on and adiabatically

22. 1.Defining slowly varying operators
2.Adiabatically eliminating fast-rotating terms
3.Solving Maxwell-Bloch equation

23. converting the excitations into pure spin-wave form
usual situation in EIT
converting the excitations into pure spin-wave form
pulse becomes trapped and evolves under nonlinear eq.
pulse propagates undistorted until exiting the fiber
Nature Physics 4, 884 (2008)

24. Bosonic operator
Generalize to the case of and which
propagate towards the left and right directions.
The counter-propagating control fields will form the standing wave and trap the quantum fields.

25. Tonks-Girardeau regime
Nature Physics 4, 884 (2008)

26. Our model : the couplings of , Type a atom Type b atom
arXiv:
: the couplings of ,
to transitions for a and b
atoms, respectively
Type a atom
Type b atom
and : detunings of
from transitions
and

27. The Hamiltonian of the system is:
quantum field
classical field

28. Type a atom
where
and
Type b atom
Group velocity:

29. and are velocities of charge and spin, respectively.
where
and
and are velocities of charge and spin, respectively.
The difference between two velocities results in the spin charge separation.
Here,
and
PRA 77, (2008)

30. Conditions
and
with
Fourier transformation of density-density correlation function
Two peaks charge velocity and spin velocity
Parameters:

31. For smaller

32. Conclusion
The spin-charge separation is simulated in one dimensional hollow-core fiber system, where the light-matter excitations, the dark-state polaritons are shown to follow the Lieb-Liniger dynamics of a quantum liquid.

33. Thank you!

34. Festchriff in honor of Vladimir Korepin May in conjunction with 5th  International Workshop on Solid State Quantum Computing and

35. favoured