1 / 30

Unconventional Josephson junction arrays for qubit devices.

Unconventional Josephson junction arrays for qubit devices. Giacomo Rotoli. Superconductivity Group & INFM Coherentia Dipartimento di Energetica, Università di L’Aquila ITALY. Collaborations: F. Tafuri, Napoli II A. Tagliacozzo, A. Naddeo, P. Lucignano, I. Borriello, Napoli I.

marcel
Télécharger la présentation

Unconventional Josephson junction arrays for qubit devices.

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Unconventional Josephson junction arrays for qubit devices. Giacomo Rotoli Superconductivity Group & INFM Coherentia Dipartimento di Energetica, Università di L’Aquila ITALY Collaborations: F. Tafuri, Napoli II A. Tagliacozzo, A. Naddeo, P. Lucignano, I. Borriello, Napoli I Jacksonville, October 5 2004

  2. Superconductivity GroupApplied Physics DivisionDipartimento di EnergeticaL’Aquila We are here Gran Sasso range (2914 m/9000 ft) and L’Aquila

  3. 1D open unconventional arrays 001 103 Building block: the two-junction loop conventional loop for small b (use g Eq) • dia, g(0)=0 g+ p-loop for small b • g+ para, g- dia, moreover there are spontaneous currents for f going to zero, i.e., g+(0)=1 and g-(0)=-1 g-

  4. 1D open unconventional arrays p p p 0 p 0 p +SF +SF +SF Chain of ½ Flux quanta or Semi-fluxons (SF) -SF -SF -SF Model: 1D GB Long Josephson Junction with presence of p-sections alternanting with conventional sections. This is equivalent to have localized p-loops in a 1D array Quest: what is the fundamental state in zero field ?

  5. 1D open unconventional arrays 0 p 0 p Quest: what is the effect of the magnetic field ? screening current adds Two solutions are no longer degenerate! Red ones is paramagnetic and have a lower energy with respect to Blue ones which is diamagnetic and with higher energy…

  6. Total energy Total energy is the sum of Josephson and magnetic energy We can write Moreover, using flux quantization, Magnetic energy is written Where b = 2pI0L/F0 . With Djj=jj-jj-1+2pnj we obtain

  7. The winding number The quantum number nj is typically zero for open arrays because the variations of the phases are small if b is not Large. On the other hand, in an annular array the last loop nN=n play the role of winding number of the phase, i.e., the number of flux quanta into the annulus.

  8. 1D open unconventional arrays Q: How we find phases ji ? A: Solving Discrete Sine-Gordon equation (DSG) With jN+2=j0=0, i+=i,i-=i-1,fN+1=f0=0 We assumefconstant, i.e.,fi=f , moreover (see E. Goldobin et al., Phys. Rev. B66, 100508, 2002; J. R. Kirtley et al., Phys. Rev. B56, 886, 1997)

  9. 1D open unconventional arrays b=Dx2/lJ2t(1 mm)2/(5 mm)2=0.04 Grain size Josephson length G. Rotoli PRB68, 052505, 2003 hd • 0-p junction (equal length) • diamagnetic sol • paramagnetic sol • N=63, b=0.04 Mean magnetization for different GBLJJs: symmetric 0-p => circles

  10. Previous work on 1D open unconventional arrays (c) (b) (a) (a) (b) (c) G. Rotoli PRB68, 052505, 2003 • N=255, b=0.04 • with 15 p-loops • 7 dia + 8 para • 5 dia + 10 para • 3 dia + 12 para • (b) and (c) corresponds to • a pre-selection of paramagnetic • solutions due to FC FC can be introduced assuming that it flips some SF from dia to para state

  11. Other papers in unconv. arrays and junctions F. Tafuri and J. R. Kirtley, Phys. Rev. B62, 13934, 2000; Tilt-Twist 45 degree YBCO GB junctions sample diamagnetic with ½ half flux quanta pinned to defects and along GB, paramagnetism only local F. Lombardi et al., Phys. Rev. Lett. in print, 2002; Tilt-Twist GB junctions with angles betw 0 and 90 rich structure of spontaneous currents for 0/90 GB Il’ichev et al., to be subm. Phys. Rev. B, 2002; First paramagnetic signal recorded, very flat GB form 45 deg asymmetric twist junctions, no spontaneous currents have been experimentally observed H. J. H. Smilde et al., Phys. Rev. Lett. 88, 057004, 2002; Artificial “zig-zag” LTC-HTC arrays

  12. 1D open unconventional arrays 001 103 lJ lL Some estimate of demag field: hd Hd(a)=7.6 mG Hd(b)=36 mG Hd(c)=80 mG we use lL=lc-axis equal to 5 mm Note that in (a) fields are of the same order of magnitude cited in Tafuri and Kirtley (lc-axis=5.9 mm)

  13. 0-p Annular JJ arrays • Have properties similar to the Annular Josephson junction • So can be thinked are related to “fluxon qubit” (A. Ustinov, • Nature 425, 155, 2003) • 2) Will have some “protection” from external perturbation • In the limit of large N (Doucout et al., PRL90, 107003, 2003) • 3) Can be build using p-junctions as in Hilgenkamp et al., • Nature 50, 422, 2003 Merging together these three ideas we have 1 qubit 2 qubit

  14. Annular arraysA practical layout N = 8 array, with CF (control field) CB (control barrier) CN (control loop N)

  15. 0-p Annular JJA DSG Q: How we find phases ji ? A: Solving Discrete Sine-Gordon equation (DSG) for the ring With jN+1=j1+2pn, n is the winding number i+=i,i-=i-1 Afconstant do no longer apply, f have to be not uniform to have effect on a 0-p AJJA

  16. Fundamental states in AJJA Spin notation

  17. AJJA arrays (excited states) N = 2 & 4 N = 6 n = 0 n = 1

  18. AJJA (excited states) (2) K-AK states large b small b Fractionalization phenomenon

  19. 0 – p Annular long junction E. Goldobin et al. PRB66, 100508, 2002 E. Goldobin et al. PRB67, 224515, 2003 E. Goldobin et al. cond-mat/0404091 (ring) Fund. state k0-p boundaries N/k sections

  20. LJJ case 0-p JJ l/k=2 (nor. length of sections) l/k=1 K = 2,4 N=32,64 k=6 N=96

  21. Annular arrays in magnetic field I Single loop (Cn) frustation on an N=16 array Frustation over loops 10-16 On an N=16 array

  22. Annular arrays in magnetic field II Critical field for flip between fund. states Frustation applied via CF is independent of N and induce a flip between para-dia sol. at h=2.1 Effect of frustation applied via a single loop, say C1, decrease with N

  23. Magnetic behavior of annular 0-p LJJ The effect of field in LJJ case is very similar

  24. Magnetic behavior for different spatial configuration Variation of fundamental state energy for different values of b and Magnetic field In the N=16 and N=64 AJJA Top: magnetic field in a single loop Bottom: magnetic field over 7 loops

  25. Annular arrays: flip dynamics N=256, k=16 array via s-type control N = 16 array via C1

  26. The process (classical) Classically it is possible to flip an half-flux quantum adding it a full flux quantum (fluxon) E. Goldobin et al. cond-mat/0404091 motion direction Successive time plot of annihilation of a fluxon on a 0-p boundary where a positive half-flux quantum was localized. Annihilation ends in a negative half flux quantum + radiation

  27. The process (quantum) Calculation for quantum process in collaboration With A. Tagliacozzo, A. Naddeo and I . Borriello (Napoli I) is in progress… The flip process is approximated summing up the analytical expression for fluxon (kink) and a localized half-flux quantum with kink velocity As free parameter to be used in a variational approach. Next step is the calculation of euclidean action for the flip, its minimization will give the result.

  28. p-Junction realization There are essentially three way to fabricate p-junctions: dIdYBCO made have the best performances in dissipation and recently show also MQT effect (collaboration Napoli II, F. Tafuri + Chalmers, T. Cleason) dissipation are good (100 W) control of currents and capacity not so easy dIs used by Hilgenkamp et al. in “zigzag” arrays, are YBCO-Nb ramp edge junctions dissipation are intermediate (20 W), control on other parameters is good SFS these are Nb-(Ni-Cu)-Nb junctions which show a phase shift depending on F barrier thickness dissipation is high at moment, critical currents and capacitance can be controlled in a fine manner

  29. Conclusion • Annular unconventional arrays and their LJJ counterpart the annular 0-p junction are very interesting physical object condensing the properties of half-flux quantum arrays and annular junction together with some energy and topological protection properties • It is conceivable to think to a protected qubit made of unconventional arrays, which will be the simplest topologically not trivial system showing the above properties and realizable with present tecnology (conventional ring array was realized for study • breather solutions, see PRE 66, 016603, 2002) • A quantum description of flip process between half-flux quantum is in progress Part of results shown here will be submitted to ASC04 conference, Jacksonville, FL USA 3-8 october 2004 session 3EI01

  30. Acknowledgements We would like to thank F.Tafuri, A. Tagliacozzo, I. Borriello, A. Naddeo for helpful discussions and suggestions. This work was supported by Italian MIUR under PRIN 2001 “Reti di giunzioni Josephson quantistiche: aspetti teorici e loro controparte sperimentale”. Contact: e-mail => rotoli@ing.univaq.it web => http://ing.univaq.it/energeti/research/Fisica/supgru.htm

More Related