Квантовые цепи и кубиты

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1 Квантовые цепи и кубиты Твердотельные наноструктуры и устройства для квантовых вычислений Лекция 2 А.В. Устинов Karlsruhe Institute of Technology, Germany Russian Quantum Center, Russia

2 Trapped ions Degree of freedom electron energy states or spin Representation of qubit single ion Manipulation laser pulses Read out fluorescence Operation time 10-9 s Decoherence time ~ 1 s Coupling ion lattice vibrations or photons Alexey Ustinov Solid-state qubits 2

Trapping ions in ultra-high vacuum Υ 0 0 Υ 0 V cosω t + 0 ξ ψ T U r 10 mm Paul trap: trapping ions by electric field combination of dc and ac fields dynamic stabilization of charges in 2D and 3D

3 Trapping ions in ultra-high vacuum Υ 0 0 Υ 0 V cosω t + 0 ξ ψ T U r 10 mm Paul trap: trapping ions by electric field combination of dc and ac fields dynamic stabilization of charges in 2D and 3D quadrupolar fields application: single ion in frequency and time standards energy ζ trapped ion W. Paul, Rev. Mod. Phys. 62, 531 (1990) Mechanical analog of the Paul trap x W T y M Alexey Ustinov Solid-state qubits 3

4 1D ion crystal Υ 0 0 Υ 0 Ion crystal: trapped ions ξ ψ V cosω t + 0 ζ 10 mm T U r Coulomb repulsion of ions static confinement along ζ radial stabilization by ac field 1D ion crystal in a linear Paul trap M.G. Raizen, et al. Phys. Rev. A 45, 6493 (1992) Alexey Ustinov Solid-state qubits 4

A crystal of 5 beryllium ions The ions balance their mutual Coulomb repulsion with the confining force of electric fields generated from the surrounding electrodes (brown).

5 A crystal of 5 beryllium ions The ions balance their mutual Coulomb repulsion with the confining force of electric fields generated from the surrounding electrodes (brown). The ions strongly fluoresce under the application of appropriate laser radiation near 313 nm. (NIST, Boulder.) The ion ion spacing is 5 µm. Alexey Ustinov Solid-state qubits 5

6 1D ion crystal as a quantum register See Quantum bits may be stored, for example, in two spin states of each ion Quantum logic transformations can be realized using the coupling provided by the quantized vibrational modes of the ions. Individual ions in the chain can be addressed by laser beams Raman state control scheme 2 1 laser 1 laser 2 w 2 w 1 magnetic level split 0 Alexey Ustinov Solid-state qubits 6

7 Trapping and cooling neutral atoms 1. Magnetic traps 2. Optical traps 3. Combined magneto-optical traps level energy Ε ε thermal broadening rate g laser light Ε γ laser beams atom Laser cooling: Nobel Prize 1997 Doppler cooling: atoms moving out have stronger photon absorption followed by isotropic emission of photons k Atom s velocity change u = m 2 2 u + u u + k u m i.e. atom slows down when k u < 0 Alexey Ustinov Solid-state qubits 7

8 Optical lattice of atoms (S. Rolston, NIST) A pattern of crossed laser beams (right) creates an array of potential wells that can confine individual laser-cooled cold atoms (left). The atom atom separation is of the order of the optical wavelength. C. Monroe, Nature 416, 238 (2002) Alexey Ustinov Solid-state qubits 8

9 Selective lattice potential for atom qubits 0 1 (I. Deutsch, University of New Mexico.) a, Optical lattice potentials can depend (e.g., due to modulation of light polarization) on the internal state (red or blue) of the confined atom qubits. b, These complementary lattice potentials can be controlled by varying the polarization of one of the lattice light fields, shifting the interference pattern and bringing atoms together in pairs for quantum logic gates. Alexey Ustinov Solid-state qubits 9

10 Entanglement with atomic systems Possible ways to realize 2-qubit gates: Coulomb interaction (ions) 2. Overlap of wavefunctions (pushing atoms towards each other) 3. Dipole-dipole interaction over Rydberg state 4. Entanglement by interference with photons 2-qubit gates are difficult to realize for both trapped ions and neutral atoms lasers J.F. Poyatos, J.I. Cirac, and P. Zoller Fortschr. Phys. 48, 9 (2000) Alexey Ustinov Solid-state qubits 10

Entanglement between ions and photons: Trapped ions in QED cavity Two mirrors enclose the trapped ion, forming an optical cavity, within which a light field

11 Entanglement between ions and photons: Trapped ions in QED cavity Two mirrors enclose the trapped ion, forming an optical cavity, within which a light field forms a standing wave Fluorescence is observed from the side of the cavity. G. R. Guthöhrlein et al. Nature 414, 49 (2001) Alexey Ustinov Solid-state qubits 11

12 Quantum networks Atom photon quantum network A selected atom inside the top optical cavity coherently transfers its internal qubit onto a single-photon qubit in the cavity through the application of a classical laser pulse represented by the coupling (t). (by H. J. Kimble, CalTech) The coupling g is between the singlephoton field in the cavity and the atom. The single photon leaks out of the top cavity, only to be caught in the lower cavity by a time-reversed and synchronized classical laser pulse (-t). C. Monroe, Nature 416, 238 (2002) Alexey Ustinov Solid-state qubits 12

Generating entangled photons Optical parametric downconversion a An ultraviolet photon incident on a nonlinear crystal can sometimes split spontaneously into two daughter photons.

13 Generating entangled photons Optical parametric downconversion a An ultraviolet photon incident on a nonlinear crystal can sometimes split spontaneously into two daughter photons. These photons are emitted on opposite sides of the pump beam, along two cones, one of which has horizontal polarization, the other of which has vertical polarization. (A. Zeilinger, University of Vienna.) b Along the optical axis, several cone pairs can be seen. Photon pairs emitted along the intersections of the cones are entangled in polarization. Alexey Ustinov Solid-state qubits 13

14 Entanglement of large (macroscopic) number of atoms Pair of Rb vapor cells (10 12 atoms) used for storage and entanglement. A common laser beam traverses both cells, resulting in the purple fluorescence glow. Particular measurements of the polarization of the output light projects the atom collections in a 'spin-squeezed' state where the collective magnetization of the two macroscopic samples is weakly entangled. E. Polzik, Phys. World, p.33 (Sept. 2002) Alexey Ustinov Solid-state qubits 14

15 Summary on microscopic qubits Good news: Microscopic qubits (molecular spins, ions, atoms, photons) can perform quantum computation Decoherence is long enough There are many tools to control them (lasers, microwaves) Quantum information can be stored in various ways (energy states, spin orientation, polarization, etc.) Bad news: Microscopic qubits are very hard to scale up in number Integration is very difficult There is no technology available now for building large (useful) quantum circuits Setup and control tools are very complex and expensive Alexey Ustinov Solid-state qubits 15

16 Condensed matter based qubits Condensed matter qubits (besides superconductors) spins in silicon magnetic nanoparticles N-doped fullerene C 60 electrons on helium surface Quantum dots Diamond qubits Alexey Ustinov Solid-state qubits 16

17 Condensed matter qubits (non-superconducting proposals) Nuclear impurity spins in Si Electron spins and charges in quantum dots Paramagnetic ions in C 60 Magnetic clusters Electrons on liquid helium 0> 1> Alexey Ustinov Solid-state qubits 17

18 Nuclear spins of 31 P donors in 28 Si substrate: The Kane s proposal B.E. Kane, Nature 393, 133 (1998) There is a hyperfine interaction between donor electron spin and nuclear spin (qubit) 28 Si crystal (spin-free) 31 P donor atoms (spin = 1/2) Temperature of few mk Magnetic field of several Tesla Alexey Ustinov Solid-state qubits 18

19 Nuclear spin of P donors in Si (2) Qubit is a spin of 31 P nucleus embedded in silicon crystal There is a hyperfine interaction between donor electron spin and nuclear spin (qubit) Evolution and measurement of qubits performed by controlling individual electron states nearby ς > Magnetic field 28 Si 31 P Alexey Ustinov Solid-state qubits 19

20 Nuclear spin of P donors in Si (3) The spins are placed ~ 20 nm apart Interaction between qubits is mediated through the donor-electron exchange interaction A-gates and J-gates control the hyperfine and exchange interaction at qubit sites A-gate J-gate A-gate Magnetic field 28 Si 31 P 31 P B.E. Kane, Nature 393, 133 (1998) 20 nm Alexey Ustinov Solid-state qubits 20

21 Nuclear spin of P donors in Si (3) The spins are placed ~ 20 nm apart Interaction between qubits is mediated through the donor-electron exchange interaction A-gates and J-gates control the hyperfine and exchange interaction at qubit sites A-gate J-gate A-gate Magnetic field 28 Si B.E. Kane, Nature 393, 133 (1998) 20 nm Alexey Ustinov Solid-state qubits 21

22 Nuclear spin of P donors in Si (4) Status The two donor spin states have been measured using the bulk ensemble of spins in Si No single-spin experiments exist to date Rabi oscillations have not been demonstrated for single spins Unsolved problems The 31 P impurities need to be placed in a controlled way It is crucial to keep constant spacing between the 31 P donors and gates Gates introduce decoherence Alexey Ustinov Solid-state qubits 22

23 Paramagnetic ions in C 60 Can we isolate nuclear spins in a controlled way? Fullerene molecule C 60 Endohedral Fullerene A@C 60 (courtesy of W. Harneit, HMI Berlin) Alexey Ustinov Solid-state qubits 23

24 Paramagnetic ions in C 60 : simulation of ion implantation of N in C 60 Target Ion source N@C 60 N@C 70 P@C 60 Effusion cell Τ = 500 Χ (courtesy of W. Harneit, HMI Berlin) Alexey Ustinov Solid-state qubits 24

25 Atomic nitrogen in C 60 Nitrogen 4 Σ 3/2 2π 2σ 1σ 1 nm Σ = 3/2 (courtesy of W. Harneit, HMI Berlin) Alexey Ustinov Solid-state qubits 25

26 Spin lifetimes of 60 FID 10 s 1 s measurements by A. Grupp, U Stuttgart 100ms 10ms T 1 1ms 100µs T 2 solution T 1 = 120 µs T 2 = 50 µs deformation of cage due to collision 10µs T (K) solid T 1 > 1 s T 2 > 20 µs vibration of N in the C 60 cage (courtesy of W. Harneit, HMI Berlin) Chem. Phys. Lett. 272, 433 (1997) Alexey Ustinov Solid-state qubits 26

27 Spins in fullerenes Alternative idea to Kane s proposal: Replace nuclear spins by endohedral spins in fullerenes (e.g. N@C 60 ) (Image: M. Welland; W. Harneit, Phys. Rev. A 65 (2002) Alexey Ustinov Solid-state qubits 27

28 Addressing fullerene qubits magnetic field gradient induced by currents resonance frequency is shifted (courtesy of W. Harneit, HMI Berlin) Ø W. Harneit, Phys. Rev. A 65 (2002) Alexey Ustinov Solid-state qubits 28

29 Magnetic clusters Use spin of a single magnetic nanoparticle to represent whole quantum computer Manipulate spin of particle by series of radio pulses Leuenberger and Loss, Nature 410, 789 (2001) Alexey Ustinov Solid-state qubits 29

30 An idea of qubit on-chip architecture using magnetic nanoparticles Coupling circuits Josephson switches superconducting loops of micro-squids magnetic qubits (clusters/particles) J. Tejada, E. M. Chudnovsky, et al. Alexey Ustinov Solid-state qubits 30

31 Quantum computing with electrons floating above helium surface? P. Platzman and M. Dykman, Science 284, 1967 (1999). Electron states can be manipulated by microwaves and by circuits embeded in the substrate below the He film Experiments have already demonstrated single-electron detection Alexey Ustinov Solid-state qubits 31

32 Electrons on helium surface M. Dykman and P. Platzman, Fortschr. Phys. 48, 1095 (2000). Electrons are attracted to the surface by the He dielectric image potential and occupy hydrogenic states associated with motion normal to the surface with a Rydberg energy of ~ 8K Alexey Ustinov Solid-state qubits 32

33 Electron qubits on helium films Electrons are localized laterally by a microelectrode post located under each electron. The posts are spaced by d~1 mm Average distances of electron in states 0> and 1> from He surface are 11 nm and 49 nm, respectively, for small pressing e Alexey Ustinov Solid-state qubits 33

34 Summary on solid-state non-superconducting qubits Good news: There are MANY different proposals Most promising are based on spins (relatively long coherence) Micro- and nano-fabrication technology is readily available Bad news: It is very difficult to make identical spins in mesoscopic devices In spite of many (>10 2 ) theoretical papers and proposals, there are only very few experiments on single-spin solid-state qubits Alexey Ustinov Solid-state qubits 34

35 Electron spins in quantum dots (QDs) These qubits can be manipulated either electronically or optically tunneling Defined by 50-nm-wide electrostatic gates on top of AlGaAs/GaAs two-dimensional electron gas It is possible to isolate a single electron in each QD Control via electrical gates => make use of spin-tocharge conversion based on the Pauli principle obeyed by electrons no tunneling Electron charge can be used for read out Alexey Ustinov Solid-state qubits 35

36 Electron spins in quantum dots: Loss & DiVincenzo proposal D. Loss and D.P. DiVincenzo, Phys. Rev. A 57, 120 (1998) Electrically controlled quantum dot array Electrons can be moved by electrical gates into the magnetized layer to produce locally different Zeeman splitting Alternatively, local Zeeman fields can be produced by field gradient produced by a current wire => spins can be addressed individually Alexey Ustinov Solid-state qubits 36

37 Qubits based on quantum dots Charge-based states Relatively easy to control and measure Very short (~1 ns) decoherence time Poor candidates for qubits Spin-based states Control by magnetic fields Relatively long decoherence times (up to 100 µs) Hard problem: read out of a single spin state Alternative technique for readout: optical Alexey Ustinov Solid-state qubits 37

N-V centres in diamond Nitrogen is by far the most common impurity found in gem diamonds Nitrogen is responsible for the yellow and brown in diamonds. D. Awschalom et al., Sci. Amer. (Oct. 2007), p.

38 N-V centres in diamond Nitrogen is by far the most common impurity found in gem diamonds Nitrogen is responsible for the yellow and brown in diamonds. D. Awschalom et al., Sci. Amer. (Oct. 2007), p.90 N for Nitrogen V for Vacancy (missing carbon atom) N-V centres are colored centers made by the association of a nitrogen impurity and a vacancy in a diamond crystal Alexey Ustinov Solid-state qubits 38

39 Nitrogen-vacancy (NV) defect in diamond G.Balasubramanian, et al. Nature Materials 8, 383 (2009) Structure and energy level scheme of the nitrogen-vacancy defect in diamond Fluorescence microscopy image of high-purity CVD diamond containing single nitrogen-vacancy defects. Fluorescence is encoded in the color scale Alexey Ustinov Solid-state qubits 39

40 Spins in diamond spins of Nitrogen-Vacancy center (S =1, I =1) spins of Nitrogen impurities (S = 1/2, I =1) nuclear spins of 13 C (I = 1/2) N-V spin Hamiltonian (z-axis // [111]): D. Awschalom Alexey Ustinov Solid-state qubits 40

CMSC 33001: Novel Computing Architectures and Technologies. Lecture 06: Trapped Ion Quantum Computing. October 8, 2018

CMSC 33001: Novel Computing Architectures and Technologies Lecturer: Kevin Gui Scribe: Kevin Gui Lecture 06: Trapped Ion Quantum Computing October 8, 2018 1 Introduction Trapped ion is one of the physical