Experiments with Ions, Atom and Molecules实验用的离子原子与分子

1、gregynog qip meetingqip experiments with ions, atoms and moleculeschristopher foot, university of oxfordc.footphysics.ox.ac.ukobjectives of these lectures: describe qip experiments that use atomic and molecular physics (not including nmr) general requirements for a quantum gate between two qubits sp

2、in-dependent interaction review experimental techniques and some current experiments with ion in traps neutral atoms in optical lattices: simulation of condensed matter physics and qip applications recent ideas for qip with polar molecules = hybrid of atoms and ionsquantum gate - controlled operatio

3、n cnot gate: crot gate (or controlled-z gate)exercise: show how to construct a cnot gate from a controlled-z gate and 2 hadamard gates. (ex 4.17 in nielson & chuang) crot gate (or controlled-z gate) based on state-dependent (spin-dependent) interactionorinteraction0011where qubit aqubit bcomment

4、 on quantum gatesequivalent to difficult to implement since requires very precise controlof experimental timing. pushing gate laser beam exerts state-dependent force on ions harmonic trapping potential repulsivecoulomb force 10ephase factorphase differencecf. wobble gate discussed laterrepulsive att

5、ractivesummary of lecture 1: ions1. requirements for qip2. ion trap principles3. read out and quantum jumps4. manipulation of single qubit by raman transitions5. laser cooling to the lowest vibrational level6. current experimental capability in oxford and elsewhere7. survey of ideas being actively e

6、xplored in experimental groups8. how to make a computer,requirements for quantum computing excellent quality qubits q = tcoherence / tgate = 106 now realised for ions move qubits around quickly and without error high precision gate between neighbours (error = 10-4 ) single-qubit gates measurement of

7、 qubits (read out)d. deutsch, proc r soc lond a 400, 97 (1985) & 425, 73 (1989).a.steane, phys. rev. a 68, 042322 (2003) & quant. inf. comp. 2, 297 (2002).*basic ion trap methodsn.b.most of the slides in this lecture come from the ion trapping group in oxford (part of the irc)paul trapr.f. q

8、uadrupole+ end caps+trapped ions1000 volts,10 mhzend viewvxtime=axial confinement by electrostatic (quadratic) potential.radial confinement by oscillating quadrupole potential.electrostatic trapping not possible, see foot, atomic physics, oup 2005the trapaxial motional freq. of order mhzion-electrod

9、e distance = 0.1 to 1 mm7 mmalkali-like ionschoice of ion:want simple energy level structure when singly-ionisedgroup ii or other metals:x = be, ca, sr, ba, yb, cd, hgground configuration of x+ ion has electron spin s = .hyperfine structure arising from interaction of nuclear spin (nuclear magnetic

10、moment) withmagnetic field created by the unpaired electron. the hyperfine structure of ca-43, the ion used in oxford experiments, is inverteds1/2f=3f=4mf=03.2 ghzmf=+4b field-independent1st order zeeman sensitive use transition with no first-order zeeman effect, which is therefore insensitive to ma

11、gnetic field fluctuations,cf. atomic clocks. qubit coherence time of order seconds (see later)readout by fluorescence on cycling transition2s1/2f=1, mf=1f=2, mf=21.25 ghz2p3/22p1/2f=3, mf=3e.g. be+selection rules cycling transitionpm tube or ccd cameraelectron shelving or “quantum jumps”012345678901

12、00200300400500600700(d) counts per 8 mstime (s)01234567890100200300400(c)observed fluorescence signals from one (a,b), two (c) and three ions (d). (a): random telegraph (850 nm laser is left permanently on)(b-d): controlled shelving (850 nm laser pulsed on when desired) counts per 8 mstime (s)012345

13、6789050100150200250300(b) counts per 8 mstime (s)01234567890100200300400500(a) time (s)counts per 20 mstime needed to measure a qubit at 99.9% fidelity collection & photon detection efficiency e = 0.02 excited state lifetime t = 5 ns required photon count for p(error) 0.001 is 10 photons time to

14、 count 10 photons = 2 t x 10 /e = 5 m ms current experiments allow 100 m ms to 1 mspoissonian distribution of photon countscattering ratethe trapexcellent signal-to-noise in detection of individual ions7 mmcomment: there is well-developed and efficient scheme for reading out the state of ions. this

15、is not yet achieved for neutral atoms or molecules.single bit rotationsmicrowaves:u on all qubits at oncestimulated raman transition:u on a chosen individual qubit1-bit gate time 1 micro-secondraman transition2s1/2f=1, mf=1f=2, mf=21.25 ghzhyperfine structure313 nm2p3/22p1/2aom: shift 1.25 ghzvery h

16、igh-precisionand stable phaseraman transition: effective 2-level systemddw1w2g100 ghz500 mhz500 mhz10 mhz photon scattering = 10-4= 1.25 mhz(unwanted) photon scattering rate2s1/2f=1, mf=1f=2, mf=22p3/22p1/2qubit decoherence per gate timephotons scattered per gate timeprl 95, 030403 (2005)trapped ato

17、m: quantum simple harmonic motionwzwwz120wz120w0w0laser cooling of trapped ions: “sideband cooling”320wl = w0 - wz12013 1resultant thermal distribution:laser cooling a trapped ion very different to cooling of free atomsmeasure temperature of trapped ion10122pgwlcompare excitation probability of firs

18、t red sideband and first blue sidebandw0cf fig. 12.10 in foot (2005)laser cooling of trapped ions: “sideband cooling”320wl = w0 - wz12013experimentalresults:2005 oxford 0.020 field-independent transition, lasting 30ms. fa single spin-echo pulse can be used to protect the memory qubit from the residu

19、al field-sensitivity. we detect no decoherence in a 1 second experiment (ramsey fringe , right), implying an effective coherence time of .contrast 99%=10s100st2sespin-down (f=4) population (a.u.)spin-echop/2p/2( ) p1st2se 10sexerciseshow why the pulse sequence /2 - - /2 is more robust than a ramsey

20、experiment (/2 - /2 sequence) also called square root of not gatecf exercise 7.3 in foot, atomic physics not gate:entanglementspin-dependent oscillating forcedipole force in standing waveb50 mmraman beamsf laser standing wave produces an oscillating force on a pair of ions robust and “fast” to be de

21、scribed in detail laters s+s s - -( explain how state-dependence of the force arises in nextlecture. force/potential depends on the polarization of the light. )*leibfried or “wobble” gated. leibfried et. al. nature 422, 412 (2003)equivalent to controlled-notreally nice gate1. only the area, not the

22、shape of the loop matters2. non-zero ion temperature?just displace the starting point,same loop no problem3. shift of laser standing wave phase?rotate the loop about the initial pointsame loop no problemdeterministic entanglement by phase gatespin qubit (40ca ground state)stretch mode freq. 866 khzi

23、on separation 9 mm (= 22 l) = 0.35 , (/2, )/2measure/2analysis pulsepreparegatewobble gate resultsjuly 2005 data:use twin loop,fidelity 82(2)% limited largely by photon scattering(d = 30 ghz)and laser intensity noised. lucas, m. mcdonnell, s. webster, j. home, b. keitch, d. stacey, a. ramos, a. stea

24、ne tomographydeduced density matrixhence entanglement of formation e = 0.52two-qubit gates use laser-driven oscillatory motion of ions: current experiments (2 to 8 ions): fidelity 90% (97% reported) gate time 10 to 100 ms future: fidelity 99.99% (10-4 ) with good (bright and stable) lasers time 100

25、ns to 1 msrequirements for quantum computing excellent quality qubits q = tcoherence / tgate = 106 now realised for ions move qubits around quickly and without error high precision gate between neighbours (error = 10-4 ) single-qubit gates measurement of qubits (read out)d. deutsch, proc r soc lond

26、a 400, 97 (1985) & 425, 73 (1989).a.steane, phys. rev. a 68, 042322 (2003) & quant. inf. comp. 2, 297 (2002).moving information around the machine100 mmlogical information encoded in large groups of ions.qec uses a lot of parallel ops. (animated version, chuang website.)kielpinski, monroe, w

27、ineland, nature 417,709 (2002)moving ions around-already mentioned by prof knight7-zone trap, oxford/liverpool collaborationion-electrode distance = 0.7 mmtrap-trap separation = 0.8 mmtest open design conceptbuilt by university of liverpool, s. taylormoving quantum information around array of ion traps with ions transported between traps possibly use large numbers o