Op#mized Planar Penning Traps for Quantum Informa#on Studies

Transcription

1 Op#mized Planar Penning Traps for Quantum Informa#on Studies Joshua Goldman Harvard University, Dept. of Physics Gabrielse Laboratory TCP2010, Saariselkä, Finland 12 April 2010

2 Outline I. Introduc#on: Towards a Single- Electron Qubit II. Penning Traps: From Hyperbolic to Planar III. Mo#on and Detec#on: Making a Harmonic Signal IV. Opera#on of a Planar Penning Trap V. Covered and Mirror- Image Planar Penning Traps VI. Conclusion and Outlook

3 Outline I. Introduc#on: Towards a Single- Electron Qubit II. Penning Traps: From Hyperbolic to Planar III. Mo#on and Detec#on: Making a Harmonic Signal IV. Opera#on of a Planar Penning Trap V. Covered and Mirror- Image Planar Penning Traps VI. Conclusion and Outlook

4 Mo#va#on Goal: Quantum computa#on with trapped electrons Single- quantum transi#ons observed for a trapped electron spin flip cyclotron jump Peil and Gabrielse, PRL 83, 1287 (1999)

5 Mo#va#on Goal: Quantum computa#on with trapped electrons Single- quantum transi#ons observed for a trapped electron Very long coherence #mes may be possible Spin damping 1/γ spin 5 years At 100 mk and 5 T, Considerable theore#cal work on coupling schemes Array of planar Penning traps, each with one electron: Ciaramicoli, Galve, Marzoli, and Tombesi, PRA 72, (2005) Ciaramicoli, Marzoli, and Tombesi, Int. J. Mod. Phys. B 20, 1699 (2006) Ciaramicoli, Marzoli, and Tombesi, PRA 78, (2008) Zurita- Sánchez and Henkel, New J. Phys 10, (2008) Marzoli, Tombesi, Ciaramicoli, Werth, Bushev, Stahl, Schmidt- Kaler, Hellwig, Henkel, Marx, Jex Stachowska, Szawiola, and Walaszyk, J. Phys. B 42, (2009)

6 Outline I. Introduc#on: Towards a Single- Electron Qubit II. Penning Traps: From Hyperbolic to Planar III. Mo#on and Detec#on: Making a Harmonic Signal IV. Opera#on of a Planar Penning Trap V. Covered and Mirror- Image Planar Penning Traps VI. Conclusion and Outlook

7 Penning Traps Axial B + Quadrupole E B Magnetron Axial Cyclotron

8 Implementa#ons of Penning traps Ideal quadrupole Equipoten#als are hyperbolic surfaces of revolu#on

9 Implementa#ons of Penning traps Hyperbolic traps Electrodes lie along equipoten#als Van Dyck, Wineland, Ekstrom, and Dehmelt, APL 28, 446 (1976) Gabrielse, PRA 27, 2227 (1983), PRA 29, 462 (1984)

10 Implementa#ons of Penning traps Hyperbolic electrodes Equipoten#als modified by finite boundaries and compensa#on electrodes (not shown) Precision measurements of g- factors, mass ra#os

11 Implementa#ons of Penning traps Cylindrical traps

12 Implementa#ons of Penning traps Cylindrical traps Gabrielse and MacKintosh Intl. J. of Mass Spec. and Ion Proc. 57, 1 (1984)

13 Implementa#ons of Penning traps Cylindrical traps Analyze and control microwave cavity Inhibit spont. emission Calculate cavity shils Cavity- assisted sideband cooling 2006/2008 Harvard electron g- factor meas.

14 Implementa#ons of Penning traps Open- endcap cylindrical traps

15 Implementa#ons of Penning traps Open- endcap cylindrical traps Gabrielse, Haarsma, and Rolston Intl. J. of Mass Spec. and Ion Proc. 88, 319 (1989)

16 Implementa#ons of Penning traps Open- endcap cylindrical traps Axial acess Proton spin flip/ an#proton g- factor meas. An#hydrogen experiments

17 Implementa#ons of Penning traps Planar Penning traps

18 Implementa#ons of Penning traps Planar Penning traps Electrodes lie in a plane Other boundary at Stahl, Galve, Alonso, Djekic, Quint, Valenzuela, Verdú, Vogel, Werth, EPJD 32, 139 (2005) Goldman and Gabrielse, PRA (accepted), arxiv: (2010)

19 Implementa#ons of Penning traps Planar Penning traps Mul#ple traps more easily fabricated Electronics could be included on- chip Open geometry may facilitate microwave access and electron loading

20 Scalability: Cylindrical vs. Planar 0.5 cm

21 Planar Penning Traps To Date 2005: Planar Penning traps first proposed Stahl, Galve, Alonso, Djekic, Quint, Valenzuela, Verdú, Vogel, Werth, EPJD 32, 139 (2005) 2006: Electrons first trapped in planar Penning traps; axial, cyclotron, magnetron resonances observed Galve, Fernández, Werth, EPJD 40, 201 (2006) 2008: Electrons trapped in cryogenic Penning trap. Goal of detec#ng a single trapped electron was not achieved. Bushev, Stahl, Natali, Marx, Stachowska, Werth, Hellwig, Schmidt- Kaler, EPJD 50, 97 (2008) Next milestone: observa#on of a single trapped electron This work: new trap designs for much narrower resonances

22 Outline I. Introduc#on: Towards a Single- Electron Qubit II. Penning Traps: From Hyperbolic to Planar III. Mo#on and Detec#on: Making a Harmonic Signal IV. Opera#on of a Planar Penning Trap V. Covered and Mirror- Image Planar Penning Traps VI. Conclusion and Outlook

23 Mo#on in an Asymmetric Poten#al Planar trap poten#als are asymmetric about the trap center

24 Mo#on in an Asymmetric Poten#al Devia#ons from ideal quadrupole complicate detec#on: Oscilla#on is anharmonic: ω z = ω z (A) Electron mo#on induces image charges in detec#on resistor Axial mo#on in thermal equilibrium with detec#on circuit Axial amplitude fluctua#ons broaden axial resonance Crucial trap design goal: Minimize amplitude dependence of axial frequency

25 Planar Trap Parameters Choose ρ i and V i to achieve most harmonic poten#al Dimensionless quan##es:

26 Parametrizing Anharmonicity Two expansions: Poten#al Frequency Axial frequency:

27 Parametrizing Anharmonicity Lowest- order amplitude dependence of ω z : Two gap traps: a 2 = 0 cannot be achieved Three-gap traps: in principle, a 2 = a 3 = a 4 = a 5 = 0 Frequency width, to lowest order: Depends on ρ i, V i

28 Minimizing Anharmonicity Three- gap traps: Certain geometries permit many vanishing C k, a k Several op#mized biases for same geometry

29 Possible Performance Amplitude- dependence of frequency may be comparable to cylindrical traps Compare to MHz widths observed in planar traps to date Typical amplitude for cylindrical traps

30 Outline I. Introduc#on: Towards a Single- Electron Qubit II. Penning Traps: From Hyperbolic to Planar III. Mo#on and Detec#on: Making a Harmonic Signal IV. Opera#on of a Planar Penning Trap V. Covered and Mirror- Image Planar Penning Traps VI. Conclusion and Outlook

31 Laboratory Planar Traps Challenges to realizing ideal trap Finite boundary Finite gaps Same op#mal proper#es achieved with small changes to V i

32 Imperfec#ons and Tuning Electrode radii will differ from nominal Need to adjust V i in situ Cylindrical, Hyperbolic Can be orthogonalized One compensa#on poten#al Planar Cannot be orthogonalized Each bias changes ω z Two (or more) compensa#on poten#als Changes harmonicity but not axial frequency Changes axial frequency Gabrielse, Haarsma, and Rolston Intl. J. of Mass Spec. and Ion Proc. 88, 319 (1989)

33 Outline I. Introduc#on: Towards a Single- Electron Qubit II. Penning Traps: From Hyperbolic to Planar III. Mo#on and Detec#on: Making a Harmonic Signal IV. Opera#on of a Planar Penning Trap V. Covered and Mirror- Image Planar Penning Traps VI. Conclusion and Outlook

34 Covered Planar Trap Boundary: parallel conduc#ng plane Op#mizable just as three- gap trap Equally scalable Features: Array of traps with single detector Axial mo#ons could be capaci#vely coupled with cover Smaller gap poten#als

35 Mirror- image Planar Trap Features: Poten#al is symmetric about trap center Can be orthogonalized Analogous to cylindrical trap Trap planes must be aligned Does not permit parallel detec#on

36 Mirror- image Covered Trap Adiaba#cally deform a mirror- image to covered trap

37 Covered/Mirror Parameters A single choice of rela#ve geometry gives op#mized covered and mirror- image trap with the same electrodes

38 Outline I. Introduc#on: Towards a Single- Electron Qubit II. Penning Traps: From Hyperbolic to Planar III. Mo#on and Detec#on: Making a Harmonic Signal IV. Opera#on of a Planar Penning Trap V. Covered and Mirror- Image Planar Penning Traps VI. Next Steps and Conclusion

39 Trap Construc#on Copper on alumina substrate Laser- machined grooves Challenges: large aspect ra#o, field emission Incorporate in 0.1 K apparatus 50 mm

40 Summary Op#mized planar Penning trap designs suggest orders- of- magnitude narrower resonances Covered traps offer an ayrac#ve scalable op#on Mirror- image traps may help with loading We now think it should be possible to detect a single electron in a planar Penning trap, a key step toward a single- electron qubit