3. Outline

4. The goal The Hamiltonian The superfast cooling concept Results Technical issues (time allowing)

5. All cooling techniques are based on a small coupling parameter, and therefore rate limited We propose a cooling method which is potentially faster than and with no limit on cooling rate Approach adaptable to other systems (micro-mechanical, segmented traps, etc). Goal

7. The Hamiltonian Standing wave

9. Assume we can implement both and pulses We could implement the red-shift operator impulsively using infinitely short pulses via the Suzuki-Trotter approx. Cooling at the impulsive limit with and taking

10. Solution: use a pulse sequence to emulate o pulse o Wait (free evolution) o reverse-pulse [Retzker, Cirac, Reznik, PRL 94, 050504 (2005)] Intuition But, we have only have

12. But The above argument isn’t realizable: We cannot do infinite number of infinitely short pulses Laser / coupling strength is finite  Cannot ignore free evolution while pulsing  Quantum optimal control

13. How we cool Apply the pulse and the pseudo-pulse Repeat Reinitialize the ion’s internal d.o.f. Repeat Sequence Cycle

14. Optimal control 2 possible avenues: Search for an “optimal” target operator  Search for an “optimal” cooling cycle 

15. Numeric work done with QLib A Matlab package for QI & QO calculations http://qlib.info

16. Cycle ACycle BCycle C Initial phonon count357 Final phonon count0.41.271.95 after 100 cycles0.020.100.22 Cycle duration4.42.70.8 No. of X,P pulses633 No. of sequences10

17. Dependence on initial phonon count 1 application of the cooling cycle

18. Effect of repeated applications of the cooling cycles

19. Dependence on initial phonon count 25 application of the cooling cycle

20. Robustness to pulse-length noise

21. How does a cooling sequence look like?

22. The unitary transformation

23. We can do even better Cycles used were optimized for the impulsive limit Stronger coupling means faster cooling

24. We can do even better

25. Cycle ACycle BCycle C Initial phonon count357 Final phonon count0.251.011.69 after 100 cycles0.00040.0070.025 Cycle duration0.40.30.2 No. of X,P pulses633 No. of sequences10 We can do even better

26. Some additional points For linear ion traps, we can cool ions individually – not to the global ground state does not apply here, as we’re not measuring energy of an unknown Hamiltonian [Aharonov & Bohm, Phys. Rev. 122 5 (1961) ]

27. Technical issues Implementation of with 3 evolutions dependent on commutation relations Matrix exponentiation very problematic If calc. involves cut-off -s and -s doubly so  Must do commutation relations analytically BCH series for 3 exponents contains thousands of elements in first 6 orders  Computerized non-commuting algebra

28. Superfast cooling A novel way of cooling trapped particles No upper limit on speed Optimized control gives surprisingly good results, even when working with a single coupling Applicable to a wide variety of systems We will gladly help adapt to your system

29. Thank you !