Quantum metamaterial without local control

A. Shvetsov, A. M. Satanin, Franco Nori, S. Savel'ev, and A. M. Zagoskin

Phys. Rev. B 87, 235410 – Published 10 June 2013

Abstract

A quantum metamaterial can be implemented as a quantum coherent one-dimensional array of qubits placed in a transmission line. The properties of quantum metamaterials are determined by the local quantum state of the system. Here we show that a spatially periodic quantum state of such a system can be realized without direct control of the constituent qubits, by their interaction with the initializing (“priming”) pulses sent through the system in opposite directions. The properties of the resulting quantum photonic crystal are determined by the choice of the priming pulses. This proposal can be readily generalized to other implementations of quantum metamaterials.

Received 14 March 2013

DOI:https://doi.org/10.1103/PhysRevB.87.235410

Authors & Affiliations

A. Shvetsov^1,*, A. M. Satanin¹, Franco Nori^2,3, S. Savel'ev^3,4, and A. M. Zagoskin^3,4,†

¹Nizhny Novgorod State University, Gagarin Avenue, 23, 603950, Nizhny Novgorod, Russia
²Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040, USA
³CEMS, RIKEN, Saitama 351-0198, Japan
⁴Department of Physics, Loughborough University, Loughborough LE11 3TU, United Kingdom

^*alexshdze@mail.ru
^†a.zagoskin@lboro.ac.uk

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 87, Iss. 23 — 15 June 2013

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
1D quantum metamaterial in a superconducting transmission line. The superconducting islands ( $S$ ) sandwiched between the superconducting strips form charge qubits ( $1 \leq n \leq N$ ); $D$ is the distance between the strips ( $S$ ), and $L_{0}$ is the distance between the qubits. In the passive (in and out) regions, with $n \leq 0$ and $n > N$ , respectively, the transmission line parameters are chosen to optimize impedance matching with the active (metamaterial) section. The electromagnetic pulse propagates along the $z$ axis, $\vec{A}$ is the vector potential, and $\vec{H}$ is the magnetic field of the electromagnetic wave.Reuse & Permissions
Figure 2
The priming or initializing pulses located in the passive regions of the waveguide line at the initial moment of time. The active region is in the center of the line between the two vertical dotted lines. The pulse parameters are $\tilde{υ} = c$ , $ω = ɛ / 2$ , $Δ = 0.18 ɛ$ , $k = (1 / 25) (2 π / L_{0})$ . The pulse width is $l = 240 L_{0}$ , and the pulse amplitude $A = 0.18$ . The matrix elements are $d_{00} = 0.4 ℏ ɛ$ , $d_{11} = 3.6 ℏ ɛ$ , and $d_{01} = 0.2 ℏ ɛ$ . The total length of the system simulated here is $\tilde{L} = 2048 L_{0}$ .Reuse & Permissions
Figure 3
Periodically modulated population of the excited levels of qubits after passing the priming or initializing pulses through the system. The period of modulation, $13 L_{0} \approx λ / 2$ , shows that this is due to the interference between these pulses. The slight aperiodicity is caused by the finite width of the pulse.Reuse & Permissions
Figure 4
Normalized dispersion relation $ω (k)$ for the quantum photonic crystal. Due to the space periodicity of $χ (z)$ , gaps open in the spectrum. Their positions and magnitude depend on $L_{m}$ and $\tilde{χ}$ . This allows to control the parameters of the quantum photonic crystal by varying the quantum states of the qubits. The graph is plotted for $L_{m} = 25 L_{0} / 2$ , $d_{00} = 0.4 ℏ ɛ$ , $d_{11} = 3.6 ℏ ɛ$ , $d_{01} = 0.2 ℏ ɛ$ , and $\tilde{υ} = c$ . The qubit population is the same as in Fig. 3.Reuse & Permissions
Figure 5
Probe pulse propagation through a spatially periodic quantum metamaterial prepared by the priming pulses. The vertical dotted lines indicate the location of the chain of qubits (i.e., the actual metamaterial). The metamaterial parameters are the same as in Fig. 2; $d_{00} = 0.4 ℏ ɛ$ , $d_{11} = 3.6 ℏ ɛ$ , $d_{01} = 0.2 ℏ ɛ$ ; the qubit population is the same as in Fig. 3. (a) The probe pulse at $t = 0$ . The pulse parameters are as follows: amplitude $A = 2 \times 10^{- 3}$ , width $l = 240 L_{0}$ , carrier frequency $ω = ɛ / 2$ , and velocity $\tilde{υ} = c$ . (b) Field distribution at $t = 500 ɛ^{- 1}$ . The partial pulse transmission is due to the finite pulse width. (c) Field distribution at $t = 500 ɛ^{- 1}$ for a probe pulse with frequency above the band gap. The pulse parameters at $t = 0$ are the same as above, except the carrier frequency now is $ω = 0.6 ɛ$ .Reuse & Permissions

Physical Review B

covering condensed matter and materials physics