Superfast Cooling Concept for Trapped Particles

2. Superfast Cooling Shai Machnes Tel-Aviv University Alex Retzker, BenniReznik, Andrew Steane, Martin Plenio

3. Outline • The goal • The Hamiltonian • The superfast cooling concept • Results • Technical issues (time allowing)

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

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

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

18. Effect of repeated applicationsof 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 meansfaster cooling

24. We can do even better

25. 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 !