We theoretically investigate the coupling of a single electron in a planar Penning trap with a remote superconducting microwave (MW) cavity. Coupling frequencies around MHz can be reached with resonators with a loaded quality factor of , allowing for the strong coupling regime. The electron and the cavity form a system of two coupled quantum harmonic oscillators. This is a hybrid and linear microwave quantum network. We show that the coherent interaction can be sustained over distances of a few mm up to several cm. Similar to classical linear MW circuits, the coherent quantum exchange of photons is ruled by the impedances of the electron and the cavity. As one concrete application, we discuss the entanglement of the cyclotron motions of two electrons located in two separate traps.
References
1.
S.
Peil
and G.
Gabrielse
, “Observing the quantum limit of an electron cyclotron: QND measurements of quantum jumps between Fock states
,” Phys. Rev. Lett.
83
, 1287
–1290
(1999
).2.
H. G.
Dehmelt
, “Continuous Stern-Gerlach effect: Principle and idealized apparatus
,” Proc. Natl. Acad. Sci. U. S. A.
83
, 2291
–2294
(1986
).3.
G.
Gabrielse
and H.
Dehmelt
, “Observation of inhibited spontaneous emission
,” Phys. Rev. Lett.
55
, 67
–70
(1985
).4.
G.
Ciaramicoli
, I.
Marzoli
, and P.
Tombesi
, “Scalable quantum processor with trapped electrons
,” Phys. Rev. Lett.
91
, 017901
(2003
).5.
G.
Ciaramicoli
, I.
Marzoli
, and P.
Tombesi
, “Quantum spin models with electrons in Penning traps
,” Phys. Rev. A
78
, 012338
(2008
).6.
G.
Ciaramicoli
, I.
Marzoli
, and P.
Tombesi
, “From a single- to a double-well Penning trap
,” Phys. Rev. A
82
, 044302
(2010
).7.
A.
Cridland
, J.
Lacy
, J.
Pinder
, and J.
Verdú
, “Single microwave photon detection with a trapped electron
,” Photonics
3
, 59
(2016
).8.
J.
Verdú
, “Theory of the coplanar waveguide Penning trap
,” New J. Phys.
13
, 113029
(2011
).9.
10.
J.
Pinder
and J.
Verdú
, “A planar Penning trap with tunable dimensionality of the trapping potential
,” Int. J. Mass Spectrom.
356
, 49
(2013
).11.
L. E.
Estes
, T. H.
Keil
, and L. M.
Narducci
, “Quantum-mechanical description of two coupled harmonic oscillators
,” Phys. Rev.
175
, 286
–299
(1968
).12.
G.
Romero
, J. J.
García-Ripoll
, and E.
Solano
, “Microwave photon detector in circuit QED
,” Phys. Rev. Lett.
102
, 173602
(2009
).13.
K.
Inomata
, Z.
Lin
, K.
Koshino
, W. D.
Oliver
, J.-S.
Tsai
, T.
Yamamoto
, and Y.
Nakamura
, “Single microwave-photon detector using an artificial [lambda]-type three-level system
,” Nat. Commun.
7
, 12303
(2016
).14.
J.
Pinder
, “The geonium chip: Engineering a scalable planar Penning trap
,” Ph.D. thesis (University of Sussex
, 2017
).15.
J. H.
Lacy
, “Development of a planar magnetic field source for the geonium chip Penning trap
,” Ph.D. thesis (University of Sussex
, 2019
).16.
J. H.
Lacy
, A.
Cridland
, J.
Pinder
, A.
Uribe
, R.
Willetts
, and J.
Verdú
, “Superconducting flux pump for a planar magnetic field source
,” IEEE Trans. Appl. Supercond.
30
, 1
–12
(2020
).17.
M.
Reagor
, H.
Paik
, G.
Catelani
, L.
Sun
, C.
Axline
, E.
Holland
, I.
Pop
, N.
Masluk
, T.
Brecht
, L.
Frunzio
, M.
Devoret
, L.
Glazman
, and R.
Schoelkopf
, “Reaching 10 ms single photon lifetimes for superconducting aluminum cavities
,” Appl. Phys. Lett.
102
, 192604
(2013
).18.
D.
Bogorin
, M.
Ware
, D.
McClure
, S.
Sorokanich
, and B.
Plourde
, “Reducing surface loss in 3D microwave copper cavities for superconducting transmon qubits
,” in IEEE 14th International Superconductive Electronics Conference, ISEC
(2013
), p. 6604283
.19.
L.
Frunzio
, A.
Wallraff
, D.
Schuster
, J.
Majer
, and R.
Schoelkopf
, “Fabrication and characterization of superconducting circuit QED devices for quantum computation
,” IEEE Trans. Appl. Supercond.
15
, 860
–863
(2005
).20.
A.
Megrant
, C.
Neill
, R.
Barends
, B.
Chiaro
, Y.
Chen
, L.
Feigl
, J.
Kelly
, E.
Lucero
, M.
Mariantoni
, P. J. J.
O'Malley
, D.
Sank
, A.
Vainsencher
, J.
Wenner
, T. C.
White
, Y.
Yin
, J.
Zhao
, C. J.
Palmström
, J. M.
Martinis
, and A. N.
Cleland
, “Planar superconducting resonators with internal quality factors above one million
,” Appl. Phys. Lett.
100
, 113510
(2012
).21.
A.
Blais
, R.-S.
Huang
, A.
Wallraff
, S. M.
Girvin
, and R. J.
Schoelkopf
, “Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation
,” Phys. Rev. A
69
, 062320
(2004
).22.
D. I.
Schuster
, A. P.
Sears
, E.
Ginossar
, L.
DiCarlo
, L.
Frunzio
, J. J. L.
Morton
, H.
Wu
, G. A. D.
Briggs
, B. B.
Buckley
, D. D.
Awschalom
, and R. J.
Schoelkopf
, “High-cooperativity coupling of electron-spin ensembles to superconducting cavities
,” Phys. Rev. Lett.
105
, 140501
(2010
).23.
D. I.
Schuster
, A.
Fragner
, M. I.
Dykman
, S. A.
Lyon
, and R. J.
Schoelkopf
, “Proposal for manipulating and detecting spin and orbital states of trapped electrons on helium using cavity quantum electrodynamics
,” Phys. Rev. Lett.
105
, 040503
(2010
).24.
D. I.
Schuster
, L. S.
Bishop
, I. L.
Chuang
, D.
DeMille
, and R. J.
Schoelkopf
, “Cavity QED in a molecular ion trap
,” Phys. Rev. A
83
, 012311
(2011
).25.
H.
Wu
, R. E.
George
, J. H.
Wesenberg
, K.
Mølmer
, D. I.
Schuster
, R. J.
Schoelkopf
, K. M.
Itoh
, A.
Ardavan
, J. J. L.
Morton
, and G. A. D.
Briggs
, “Storage of multiple coherent microwave excitations in an electron spin ensemble
,” Phys. Rev. Lett.
105
, 140503
(2010
).26.
Y.
Kubo
, C.
Grezes
, A.
Dewes
, T.
Umeda
, J.
Isoya
, H.
Sumiya
, N.
Morishita
, H.
Abe
, S.
Onoda
, T.
Ohshima
, V.
Jacques
, A.
Dréau
, J.-F.
Roch
, I.
Diniz
, A.
Auffeves
, D.
Vion
, D.
Esteve
, and P.
Bertet
, “Hybrid quantum circuit with a superconducting qubit coupled to a spin ensemble
,” Phys. Rev. Lett.
107
, 220501
(2011
).27.
Z.-L.
Xiang
, S.
Ashhab
, J. Q.
You
, and F.
Nori
, “Hybrid quantum circuits: Superconducting circuits interacting with other quantum systems
,” Rev. Mod. Phys.
85
, 623
–653
(2013
).28.
N.
Daniilidis
, D. J.
Gorman
, L.
Tian
, and H.
Häffner
, “Quantum information processing with trapped electrons and superconducting electronics
,” New J. Phys.
15
, 073017
(2013
).29.
R. N.
Simons
and R.
Arora
, “Coupled slot line field components
,” IEEE Trans. Microwave Theory Tech.
30
, 1094
(1982
).30.
S.
Anlage
, V.
Talanov
, and A.
Schwartz
, Principles of Near-Field Microwave Microscopy
(Springer-Verlag
, New York
, 2007
), Vol. 1
, pp. 215
–253
.31.
H. G.
Dehmelt
and F. L.
Walls
, “Bolometric technique for the RF spectroscopy of stored ions
,” Phys. Rev. Lett.
21
, 127
–131
(1968
).32.
A.
Al-Rjoub
and J.
Verdú
, “Electronic detection of a single particle in a coplanar-waveguide Penning trap
,” Appl. Phys. B
107
, 955
(2012
).33.
D.
Hanneke
, S.
Fogwell
, and G.
Gabrielse
, “New measurement of the electron magnetic moment and the fine structure constant
,” Phys. Rev. Lett.
100
, 120801
(2008
).34.
S.
Sturm
, A.
Wagner
, B.
Schabinger
, J.
Zatorski
, Z.
Harman
, W.
Quint
, G.
Werth
, C. H.
Keitel
, and K.
Blaum
, “g factor of hydrogenlike
,” Phys. Rev. Lett.
107
, 023002
(2011
).35.
S.
Ulmer
, C. C.
Rodegheri
, K.
Blaum
, H.
Kracke
, A.
Mooser
, W.
Quint
, and J.
Walz
, “Observation of spin flips with a single trapped proton
,” Phys. Rev. Lett.
106
, 253001
(2011
).36.
S.
Ulmer
, H.
Kracke
, K.
Blaum
, S.
Kreim
, A.
Mooser
, W.
Quint
, C. C.
Rodegheri
, and J.
Walz
, “The quality factor of a superconducting RF resonator in a magnetic field
,” Rev. Sci. Instrum.
80
, 123302
(2009
).37.
W. M.
Itano
, J. C.
Bergquist
, J. J.
Bollinger
, and D. J.
Wineland
, “Cooling methods in ion traps
,” Phys. Scr.
T59
, 106
–120
(1995
).38.
J.
Bartlett
, G.
Hardy
, and I.
Hepburn
, “Performance of a fast response miniature adiabatic demagnetisation refrigerator using a single crystal tungsten magnetoresistive heat switch
,” Cryogenics
72
, 111
–121
(2015
).39.
J.-H.
Yeh
, J.
Lefebvre
, S.
Premaratne
, F.
Wellstood
, and B.
Palmer
, “Microwave attenuators for use with quantum devices below 100 mK
,” J. Appl. Phys.
121
, 224501
(2017
).40.
Z.
Wang
, S.
Shankar
, Z.
Minev
, P.
Campagne-Ibarcq
, A.
Narla
, and M.
Devoret
, “Cavity attenuators for superconducting qubits
,” Phys. Rev. Appl.
11
, 014031
(2019
).41.
42.
43.
K.
Brown
, C.
Ospelkaus
, Y.
Colombe
, A.
Wilson
, D.
Leibfried
, and D.
Wineland
, “Coupled quantized mechanical oscillators
,” Nature
471
, 196
–199
(2011
).44.
J.
Winters
and C.
Rose
, “High-Tc superconductor waveguides: Theory and applications
,” IEEE Trans. Microwave Theory Tech.
39
, 617
–623
(1991
).45.
J.
Krupka
, K.
Derzakowski
, M.
Tobar
, J.
Hartnett
, and R. G.
Geyer
, “Complex permittivity of some ultralow loss dielectric crystals at cryogenic temperatures
,” Meas. Sci. Technol.
10
, 387
(1999
).46.
A.
Chizhov
, E.
Schmidt
, L.
Knöll
, and D.-G.
Welsch
, “Propagation of entangled light pulses through dispersing and absorbing channels
,” J. Opt. B
3
, 77
(2001
).47.
D. L.
Moehring
, P.
Maunz
, S.
Olmschenk
, K. C.
Younge
, D. N.
Matsukevich
, L. M.
Duan
, and C.
Monroe
, “Entanglement of single-atom quantum bits at a distance
,” Nature
449
, 68
–71
(2007
).48.
B. R.
Johnson
, M. D.
Reed
, A. A.
Houck
, D. I.
Schuster
, L. S.
Bishop
, E.
Ginossar
, J. M.
Gambetta
, L.
DiCarlo
, L.
Frunzio
, S. M.
Girvin
, and R. J.
Schoelkopf
, “Quantum non-demolition detection of single microwave photons in a circuit
,” Nat. Phys.
6
, 663
–667
(2010
).49.
L.
Lamata
, D.
Porras
, J. I.
Cirac
, J.
Goldman
, and G.
Gabrielse
, “Towards electron-electron entanglement in Penning traps
,” Phys. Rev. A
81
, 022301
(2010
).50.
S.
Geaney
, D.
Cox
, T.
Hönigl-Decrinis
, R.
Shaikhaidarov
, S.
Kubatkin
, T.
Lindström
, A.
Danilov
, and S.
de Graaf
, “Near-field scanning microwave microscopy in the single photon regime
,” Sci. Rep.
9
, 12539
(2019
).© 2020 Author(s).
2020
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