Disclaimer

1. Disclaimer • This collection of slides is for reference only, in connection with the workshop at which it was presented. It is not intended as a complete review or a definitive overview of the field, but only as a presentation of some material that might be helpful. The opinion slides that follow the “End” are the opinion of the author and are not necessarily those of NIST or of the US government. Please do not use or reproduce any of the material from this presentation without the permission of the author. Please see disclaimer at beginning of slides

2. William D. Phillips Joint Quantum Institute National Institute of Standards and Technology, Gaithersburg, MD University of Maryland, College Park, MD NIST/JQI Laser Cooling and Trapping Group: Kris Helmerson, Paul Lett, Trey Porto, Ian Spielman Quantum information, computing, and simulation with cold atoms I will present some of the state-of-the-art internationally, including work in the NIST/JQI Laser Cooling and Trapping Group, along with my personal perspectives. $upport: DARPA, IARPA, JQI, NIST, NSF (PFC), ONR Please see disclaimer at beginning of slides

3. Quo Vadis Cold Atoms? Enticing themes for the future with cold atoms: Many-body entanglement Strongly correlated systems Large scale systems married with control and measurement that spans bulk properties and individual particles and correlations. Engineering a different class of Hamilltonian—exotic kinds of matter (e.g., topological matter) Please see disclaimer at beginning of slides

4. Why Cold (Neutral) Atoms? As Qubits As Simulators • Excellent coherence—clocks • Known Hamiltonian • Optical information transfer • High qubit density • Mobility: arbitrary pair entanglement • Both individual and massively parallel operations • Plentiful fresh qubits—important for error correction • Choice of qubit basis • High-fidelity, fast single-qubit operations, detection • etc. • Optical lattices are flexible and reconfigurable • Choice of dimensionality, quantum statistics, lattice type (even quasi-periodic) • Tunneling and interactions are tunable • Lattices are near-perfect: no phonons, no dislocations • Non-lattice applications • Measurements: velocity, coherence, correlations, … Simulation can be to realize a mathematical model or to mimic a physical system. Please see disclaimer at beginning of slides

5. Optical Lattice Optical Tweezers Tweezers and lattices • Versatile and agile • Address a single atom or several nearby atoms • Induce state changes or entangle atoms • Move atoms to distant locations • Prepare large numbers of initialized atomic qubits • Store a large number of atoms in a small space • Perform identical operations on large numbers of atoms Please see disclaimer at beginning of slides

6. DiVincenzo Criteria (5+2) 1. Well defined extendible qubit array; stable memory 2. Initialization of the qubits 3. Long decoherence time—much longer than gate time 4. Universal set of gate operations 5. Qubit-specific quantum measurements (Cold atoms have, with varying degrees of fidelity, in various laboratories, achieved all of these) 6.Interconvert stationary and flying qubits 7.Transmit flying qubits from place to place (Information exchange from atoms to photons is more natural than with some other kinds of qubits. See “The Quantum Internet,” H. J. Kimble, Nature (2008), and his talk here. Please see disclaimer at beginning of slides

7. Initializing lots of cold-atom qubits Mott insulator first observed with cold atoms by I. Bloch et al. in Munich ‘02 “superfluid” phase BEC ( commensurate filling ) Bose-Einstein Condensate (1995 NIST/JILA and MIT; Nobel 2001); millions of atoms in the same quantum state. deeper lattice NIST/JQI 2-D Mott insulator, Spielman et al. 2007 lattice spacing ~ 0.4 mm Please see disclaimer at beginning of slides tunneling << on site interaction tunneling >> on site interaction

8. Entangling adjacent atoms in a lattice (Hansch group (Munich/Garching); Bloch, Greiner, et al.) (Following a suggestion by Cirac and Zoller) In the long chain of atoms—one per site due to the Mott transition—not pairwise entanglement, but cluster entanglement results (useful for measurement-based quantum computation). Please see disclaimer at beginning of slides

9. Swap Movie quantum SWAP of isolated pairs NIST/JQI Please see disclaimer at beginning of slides SWAP movie

10. Swap oscillations: Porto Group at NIST/JQI no decoherence during many SWAP oscillations Fidelity > 64% 0.5 1.0 1.5 milliseconds is a “universal” 2-qubit entangling gate Please see disclaimer at beginning of slides

11. Swap oscillations: Porto Group at NIST/JQI no decoherence during many SWAP oscillations Fidelity > 64% 0.5 1.0 1.5 milliseconds is a “universal” 2-qubit entangling gate But all of these lattice entangling operations detect many qubits or pairs of qubits at once Please see disclaimer at beginning of slides

12. Quantum gas microscope: Greiner Group, Harvard High-resolution imaging just resolves atoms in adjacent lattice sites. lattice spacing = 600 nm Please see disclaimer at beginning of slides

13. Weiss lattice 4.9 μm 3D Optical Lattice with Large Spacing (Weiss Group, Penn State) θ=10° With these large lattice spacings, atoms can be individually addressed and pairwise entangled using focused laser beams (but tunnel coupling is low) Please see disclaimer at beginning of slides

14. Atom Weiss lattice photo Atoms in a large-spacing lattice at Penn State This is one plane of a 3D lattice, with random half-filling due to destruction at multiply-filled sites. Please see disclaimer at beginning of slides

15. Repairing and manipulating an atom storage register (Meschede Group, Bonn) Two perpendicular conveyor-belts • "sort" atoms • coupling between arbitrary pairs of atoms Please see disclaimer at beginning of slides

16. Sorting Atoms Falsecolortagging to guide the eye Please see disclaimer at beginning of slides

17. Sorting Atoms Please see disclaimer at beginning of slides

18. Sorting Atoms Please see disclaimer at beginning of slides

19. Sorting Atoms Please see disclaimer at beginning of slides

20. Sorting Atoms Please see disclaimer at beginning of slides

21. Sorting Atoms Please see disclaimer at beginning of slides

22. Sorting Atoms Please see disclaimer at beginning of slides

23. Sorting Atoms Please see disclaimer at beginning of slides

24. Sorting Atoms Dx ~ 15 mm Dx Dx Please see disclaimer at beginning of slides

25. Optical Tweezers Another, and more flexible, way to have individual addressing of single qubits is with optical tweezers—single focused laser beams that trap or light-shift specific atoms. Please see disclaimer at beginning of slides

26. Palaiseau tweezers Dipole trap 1 Vacuum Dipole trap 2 Trapping single atoms in optical tweezers (Grangier group—Palaiseau) Atom A lens Atom B CCD image Single qubit gate: 2 ms p-pulse, 99% Fidelity (prep.+ gate + detection); 40 ms decoherence time Move single qubits, transfer qubits between tweezers: no loss, no decoherence (in Jessen group: Fidelity (π pulse) = 0.996(3)) Please see disclaimer at beginning of slides

27. Tweezer arrays: Birkl group, Darmstadt single atoms, separately addressable and detectable microlens array illuminated uniformly with one or multiple beams or individually Shift register: atoms are shifted by one array of tweezers, transferred to another, then shifted again. Please see disclaimer at beginning of slides

28. Magnets + tweezers Another approach: magnets+tweezers Spreeuw group, U. Amsterdam B0 trapped atoms: mK 87Rb Lithographically micro-fabricated array of 1250 traps/mm2 10 mm “atom chip” (room temperature) Magnetized film: hard-disc material shift-register applied to tweezer-addressed defect hundreds of sites with 10-1000 atoms each Please see disclaimer at beginning of slides

29. Entangling distant atoms in tweezers or large-period lattices Ground-state atoms have short range, weak interactions—mainly contact interactions, so that atoms need to be on the same site to become entangled. For atoms at different sites, excitation to high Rydberg states allows fast, distant entanglement. V ~ d2/R3 R R ~ several mm A B Time to entangle ~ 1 / V << 1 ms (for high Ry states) Please see disclaimer at beginning of slides

30. Demonstrations of Ry Blockade common excitation separate excitation Palaiseau: Grangier, Browaeys… U. Wisc. Madison: Saffman, Walker,… 4 mm separation 10 mm separation Note ~ 50 ns “gate time” In both cases, the presence of an atom, some microns distant, prevents the excitation of its neighbor, because of the strong, long-range, Ry-Ry interaction energy. Please see disclaimer at beginning of slides

31. Perspectives on Quantum Computing with cold atoms • All the DiVincenzo Five criteria have been addressed. Need a lot more fidelity and scaling. No obvious roadblocks. • Need to put the pieces together in a scalable way. • There is a long way to go before a “competent” quantum computer is realized (e.g., factor numbers no other computer can factor) if ever. (remember the Phillips 50/50 analysis) • There are a lot of interesting things to do with quantum processing that do not require a competent, general purpose computer: • Quantum repeaters. This involves the DiVincenzo +2 criteria. • Quantum devices—sub-shot-noise measurement. • Testing quantum mechanics in large entangled systems. Quantum/classical interface; e.g., can 400 qubits be entangled? • Quantum simulation (we are doing it NOW!) Please see disclaimer at beginning of slides

32. Quantum Simulation Feynman legendarily noted that no classical computer can efficiently simulate a quantum system (although clever approximations abound). • Direct calculation: a competent, error corrected quantum computer will be able to do interesting quantum problems. • More modest problems might be done without error correction (even several tens of entangled objects are beyond the capability of classical computers). • The “native” Hamiltonians for cold atoms can realize models that are too hard to solve mathematically. • “New” Hamiltonians can be engineered to solve other models. • Physical systems can be approximated with cold atoms, where measurement and control capabilities provide advantages over the original systems. Please see disclaimer at beginning of slides

33. The native Hamiltonian for atoms in an optical lattice is the Hubbard model of condensed matter physics t ... tunneling U ... onsite interaction With cold atoms, one can change t/U in ways impossible in real condensed matter systems. One can undergo the Mott transition. Jaksch, Bruder, Cirac, Gardiner, Zoller, Phys. Rev. Lett. 81, 3108 (1998) Please see disclaimer at beginning of slides

34. The Mott Insulator Transition “insulator” phase “superfluid” phase first observed with cold atoms by I. Bloch et al. in Munich ‘02 deeper lattice Precision measurement at NIST/ JQI (Spielman et al. 2008) locates the 2D Bose-Hubbard phase transition that agrees with an-only-recently available high-accuracy Quantum Monte Carlo calculation. Please see disclaimer at beginning of slides

35. Another quantum phase transition, in spinor BEC Na (F = 1) spin population relaxes to the ground state. Measurement of r0 maps out the diagram with high precision. 1 0 0 0 calculated phase diagram B m 0 1 Please see disclaimer at beginning of slides (Lett group, NIST/JQI)

36. Engineered Hamiltonian: a charge in a magnetic vector potential (There are lots of other Hamiltonians to engineer in lots of ways.) Why? Study the equivalent to quantum Hall and fractional quantum Hall effects in a 2-D system: an exotic state of matter that is easily controlled and measured. How? One way is to rotate. In the rotating frame the Coriolis force mimics the Lorentz Force, but the centrifugal force causes problems. Please see disclaimer at beginning of slides quasimomentum (kphot)

37. Demonstration of a synthetic E-field Switch off the synthetic A-field, producing an impulse that kicks the atoms before kick after kick mechanical momentum Next: give the A-field a curl, to simulate a magnetic field; look for a vortex lattice, go to the quantum Hall regime. Please see disclaimer at beginning of slides

38. Cold atoms mimic a condensed system Berezinskii-Kosterlitz-Thouless transition in 2-D Dalibard group, ENS, interferes two planes of atomic gas. E. Cornell group, NIST/JILA realizes the X-Y model of K-T. Helmerson group, NIST/JQI Single plane of atoms Please see disclaimer at beginning of slides

39. Simulating a superconducting loop with cold atoms Helmerson and colleagues @ JQI Plugged trap allows persistent current in a toroidal geometry with plug without plug • Next: a simulated Josephson junction added to the circuit—atom SQUID. • No Meissner effect • Dynamically variable tunnel barrier • Vary interactions Please see disclaimer at beginning of slides

40. Something new: Atom-friendly, multi-spatial-mode squeezed light Hot atoms Group of Paul Lett at NIST/JQI Please see disclaimer at beginning of slides

41. Something new: Atom-friendly, multi-spatial-mode squeezed light Hot atoms Please see disclaimer at beginning of slides

42. Something new: Atom-friendly, multi-spatial-mode squeezed light • transfer non-classicality to atoms • continuous-variable quantum communications • faint image recovery • supersensitive detection • superresolution imaging • high-density data storage • position sensing • parallel quantum data storage • (storage of entangled images) Please see disclaimer at beginning of slides

43. Perspectives on quantum simulation • Simulations with cold atoms hold the promise of learning things about many-body quantum systems that we have not been able to learn in other ways. • (Because the problems are too hard, or other systems are not amenable to measurement and control, or similar systems simply do not exist.) • Simulations of all kinds (native and non-native realizations of models, plus analogs of CM systems) show great promise for important and interesting results. • Important contributions from simulations are already in hand (e.g. accurate quantum phase transitions, fresh look at 2-D superfluid transition) • Synthetic magnetic fields should allow study of interesting quantum Hall physics, topological matter. • Fermi-Hubbard and similar studies may elucidate high-Tc superconductivity • SQUID analogs could bring new insights into superfluid behavior and applications. • Cold atoms allow a new look at the role of dimensionality in quantum systems. • Getting lower temperature will be an important issue, with new approaches needed—bosonic cooling of fermions, algorithmic cooling, using QI techniques. • exotic spins systems (e.g.,frustrated systems, spin-glass, topological states,….) • Control the dissipation/bath as well as the conservative Hamiltonian • … Please see disclaimer at beginning of slides

44. Final Thoughts on Simulations Why cold-atom quantum simulation is interesting: • Some problems may be intractable by other means. • Interesting CM problems may be better addressed with particles whose momentum is easily measured, whose Hamiltonians and states are easily manipulated, etc. • Other kinds of physics (high-energy, cosmology,…) may have useful simulations with cold atoms in lattices or otherwise. • Things not seen in “Nature” can be easy in cold-atom system, and may teach us interesting things (e.g., certain kinds of quasiperiodic structures, fermion/boson choices, interaction choices,…) Please see disclaimer at beginning of slides

45. The End Please see disclaimer at beginning of slides

46. Some thoughts about the pursuit of research in quantum information I believe it is likely that a “really” large scale quantum computer (one that can factor numbers that cannot otherwise be factored) will be hybrid—to a larger degree than Lukin discussed in the context of NV centers. It would be a mistake to discount certain QC platforms at this stage, and probably for quite some time, as they might be key contributors to some aspect of a QI system. It would be a mistake to only support the apparent function of a particular platform that appears to be best adapted to it—Nature is perverse and experimenters are both lucky and clever. Corollary: Don’t think too hard about an experiment before you do it—you may become discouraged because you cannot imagine how clever and lucky you will be when the problem you anticipate is actually at hand. Stable funding: don’t dismiss the multiple appeals for stable funding as whining on the part of researchers who don’t like being cut. It makes a big difference in the ability to accomplish missions. Jerking people around with funding is a way to alienate some of the best people and to select in favor of mediocrity. QC in particular is a long-haul proposition. It is not the Manhattan project, and even if it could be accomplished by assigning a tremendous amount of money and people, that would probably not be the best way to do it. That doesn’t mean it is not very important. Nor do I mean that unproductive research should have continued funding. But volatility in funding could insure the failure of the mission. Please see disclaimer at beginning of slides

47. Some thoughts about the pursuit of research in quantum information Diversity of funding styles at different agencies is one of the great strengths of US science, and one that will serve the development of quantum information very well. The styles of places like NSF, DARPA, ONR,.. are very different and that is a good thing. The success of any one of those is not in itself a good reason for others to copy that style. The differences themselves have high value intrinsically. It is one of the things that helps to ensure that a brilliant, innovative idea will find a home. There are some agencies where a single program director can decide that something should be funded, and others where half a dozen outside reviewers have to rank a proposal as “excellent” for it to be funded. We are well served by having both kinds, particularly with QI, which is important and has important aspects that are not at all well-understood. Please see disclaimer at beginning of slides