1. Spin-motion coupling in atoms Cooling to motional ground states and Quantum logic spectroscopy

2. Ingredients k

3. k

4. k  Rotating frame  Rotating wave approximation

5. k

6. k

7. k

8. k

9.  Another rotating frame

10. Carrier interaction

11.  Another rotating frame Red sideband interaction Interaction strength given by

12.  Another rotating frame Blue sideband interaction Interaction strength given by

13. Resolved sideband cooling Step 1: Doppler cool Ion cooled to ground state: PRL 75, 4011 (1995) Neutral atom cooled to ground state: PRX 2, 041014(2012)

14. Resolved sideband cooling Step 1: Doppler cool Step 2: Pump to 2 S 1/2 2 P 1/2 370 nm |  |   = 20 MHz F=1 F=0 F=1 F=0 Ion cooled to ground state: PRL 75, 4011 (1995) Neutral atom cooled to ground state: PRX 2, 041014(2012)

15. Resolved sideband cooling Step 1: Doppler cool Step 2: Pump to 2 P 1/2  = 20 MHz F=1 F=0 Ion cooled to ground state: PRL 75, 4011 (1995) Neutral atom cooled to ground state: PRX 2, 041014(2012) Step 3: Apply red sideband

16. Resolved sideband cooling Step 1: Doppler cool Step 2: Pump to 2 P 1/2  = 20 MHz F=1 F=0 Ion cooled to ground state: PRL 75, 4011 (1995) Neutral atom cooled to ground state: PRX 2, 041014(2012) Step 3: Apply red sideband Step 4: Pump to

17. Resolved sideband cooling Step 1: Doppler cool Step 2: Pump to 2 P 1/2  = 20 MHz F=1 F=0 Ion cooled to ground state: PRL 75, 4011 (1995) Neutral atom cooled to ground state: PRX 2, 041014(2012) Step 3: Apply red sideband Step 4: Pump to etc Finish in … How to check?

18. Measuring phonon number Red sideband interaction strength given by Blue sideband interaction strength given by Ion cooled to ground state: PRL 75, 4011 (1995) Neutral atom cooled to ground state: PRX 2, 041014(2012) Assume thermal state with mean phonon number Probe red, blue sidebands for same duration and spin state

19. Measuring phonon number Ion cooled to ground state: PRL 75, 4011 (1995) Neutral atom cooled to ground state: PRX 2, 041014(2012) Assume thermal state with mean phonon number and spin state Before: asymmetry 1/3 After: asymmetry 1/67

20. Quantum logic spectroscopy Motivation: Probe a “clock” transition when you don’t have a cycling transition Spectroscopy ion Logic ion Science 309, 749 (2005)

21. Quantum logic spectroscopy Motivation: Probe a “clock” transition when you don’t have a cycling transition Spectroscopy ion Logic ion Science 309, 749 (2005)

22. Quantum logic spectroscopy Science 309, 749 (2005) Step 1: Initialization n=1 n=0 n=1 n=0 Be + Al +

23. Quantum logic spectroscopy Science 309, 749 (2005) Step 1: Initialization n=1 n=0 n=1 n=0 Be + Al + Step 2: Interrogate clock transition

24. Quantum logic spectroscopy Science 309, 749 (2005) Step 1: Initialization n=1 n=0 n=1 n=0 Be + Al + Step 2: Interrogate clock transition Step 3: Drive red sideband on Al

25. Quantum logic spectroscopy Science 309, 749 (2005) Step 1: Initialization n=1 n=0 n=1 n=0 Be + Al + Step 2: Interrogate clock transition Step 3: Drive red sideband on Al Step 4: Drive red sideband on Be Step 5: Read out Be

26. Quantum logic spectroscopy Science 309, 749 (2005) n=1 n=0 n=1 n=0 Be + Al +

27. Quantum logic spectroscopy: Initialization sequence n=1 n=0 m F = 1/2 m F = 3/2 Al + m F =5/2 … - Carrier transition with

28. Quantum logic spectroscopy: Initialization sequence n=1 n=0 m F = 1/2 m F = 3/2 Al + m F =5/2 … - Carrier transition with - Red sideband transition with

29. Quantum logic spectroscopy: Initialization sequence n=1 n=0 m F = 1/2 m F = 3/2 Al + m F =5/2 … - Carrier transition with - Red sideband transition with - Laser cool the motional mode (with Be)

30. Quantum logic spectroscopy: Initialization sequence n=1 n=0 m F = 1/2 m F = 3/2 Al + m F =5/2 … - Carrier transition with - Red sideband transition with - Laser cool the motional mode (with Be)

31. Other uses for spin-motion coupling Cooling oscillators to their ground state – Trapped ions, neutral atoms – Mesoscopic oscillators Making ions talk to each other – Entanglement – Spectroscopy for atomic clocks Quantum simulations – Magnetism in ions – Synthetic gauge fields in neutral atoms