Tuning the inductance of Josephson junction arrays without SQUIDs R. Kuzmin1N. Mehta1N. Grabon2and V. E. Manucharyan1 3 1Department of Physics University of Maryland College Park Maryland 20742 USA.

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Tuning the inductance of Josephson junction arrays without SQUIDs

R. Kuzmin,1N. Mehta,1N. Grabon,2and V. E. Manucharyan1, 3

1Department of Physics, University of Maryland, College Park, Maryland 20742, USA.

2Laboratory for Physical Sciences, College Park, Maryland 20740, USA.

3´

Ecole Polytechnique F´ed´erale de Lausanne (EPFL), Lausanne CH-1015, Switzerland.

(Dated: October 24, 2022)

It is customary to use arrays of superconducting quantum interference devices (SQUIDs) for im-

plementing magnetic ﬁeld-tunable inductors. Here, we demonstrate an equivalent tunability in a

(SQUID-free) array of single Al/AlOx/Al Josephson tunnel junctions. With the proper choice of

junction geometry, a perpendicularly applied magnetic ﬁeld bends along the plane of the supercon-

ductor and focuses into the tunnel barrier region due to a demagnetization eﬀect. Consequently,

the Josephson inductance can be eﬃciently modulated by the Fraunhoﬀer-type supercurrent inter-

ference. The elimination of SQUIDs not only simpliﬁes the device design and fabrication, but also

facilitates a denser packing of junctions and, hence, a higher inductance per unit length. As an

example, we demonstrate a transmission line, the wave impedance of which is ﬁeld-tuned in the

range of 4 −8 kΩ, centered around the important value of the resistance quantum h/(2e)2≈6.5 kΩ.

The arrays of Josephson junctions are widely used in

science and technology as compact on-chip low-loss ki-

netic inductors operating well into the microwave fre-

quency range. Thanks to the Josephson eﬀect, the ki-

netic inductance density in such arrays can exceed the

vacuum permeability by four orders of magnitude [1].

This property enables access to new regimes of quan-

tum ﬂuctuations in superconducting circuits [2], demon-

strations of novel superconducting qubits [3–6], as well

as applications in parametric ampliﬁcation [7–11], elec-

tromechanical transduction [12], and hybrid circuit QED

[13]. Of particular interest is the use of Josephson arrays

for creating electromagnetic vacuums with a character-

istic impedance Zexceeding the scale of the resistance

quantum RQ=h/(2e)2≈6.5 kΩ, which enable new

regimes of quantum electrodynamics [14], simulations of

quantum impurity problems [15–19], explorations of the

superconductor-insulator quantum phase transitions [20–

24], and possibly a metrology of dc current [25–30]. Fi-

nally, Josephson junction arrays are building blocks for

various wire-based Josephson metamaterials [31] with ap-

plications in tunable dielectrics [32] and dark matter de-

tectors [33].

Tuning the array’s inductance in-situ is a very useful

feature for many of the applications mentioned above, see

e.g. [34–37]. To date, a common way to tune the array’s

inductance, is to split each junction into two, forming

a SQUID array, and piercing the SQUID loops with a

global external magnetic ﬁeld. In this work, we demon-

strate an overlooked method to ﬂux-tune an array’s in-

ductance without introducing SQUIDs. Our scheme re-

lies on a demagnetization eﬀect in standard rectangular

overlap-type Josephson junctions placed in a transverse

magnetic ﬁled. As was noticed quite some time ago, a

magnetic ﬁeld perpendicular to a junction’s barrier cre-

ates demagnetizing currents in the junction’s electrodes

FIG. 1. (a) Scanning electron microscope image of a section

of a Josephson junction array. The junctions are formed by

an overlap of aluminum islands, with an example shown in

false colors (blue-top, orange-bottom), separated by a thin

barrier of aluminum oxide (not shown). Only two islands

are highlighted. Dashed arrows illustrate the magnetic ﬁeld

lines penetrating through the barrier layers when the array is

placed in a transverse magnetic ﬁeld (solid white arrows). (b)

A circuit diagram of a Josephson junction array well-described

in a long-wavelength limit as a telegraph transmission line. (c)

An optical photograph of a tunable Josephson transmission

line comprised of two parallel junction arrays (at the center)

connected to a dipole antenna on the left and to a qubit on the

right. The qubit plays the role of a probe for the transmission

line’s impedance.

[38, 39]. These currents produce a magnetic ﬁeld which

penetrates the barrier region (Fig. 1a) and modulates

the junction’s critical current Ic. Later experiments and

simulations demonstrated that the eﬀect of the transverse

magnetic ﬁeld on Icdepends strongly on the junction ge-

ometry [40, 41]. In fact, with short and wide junctions,

like in Fig. 1a, the perpendicular ﬁeld can be much more

capable in the modulation of Icthan the in-plane one

arXiv:2210.12119v1 [cond-mat.supr-con] 21 Oct 2022

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TuningtheinductanceofJosephsonjunctionarrayswithoutSQUIDsR.Kuzmin,1N.Mehta,1N.Grabon,2andV.E.Manucharyan1,31DepartmentofPhysics,UniversityofMaryland,CollegePark,Maryland20742,USA.2LaboratoryforPhysicalSciences,CollegePark,Maryland20740,USA.3EcolePolytechniqueFederaledeLausanne(EPFL),LausanneCH-10...

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Tuning the inductance of Josephson junction arrays without SQUIDs R. Kuzmin1N. Mehta1N. Grabon2and V. E. Manucharyan1 3 1Department of Physics University of Maryland College Park Maryland 20742 USA.

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