Population inversion induced by Landau–Zener transition in a strongly driven rf superconducting quantum interference device

Abstract

Microwave resonances between discrete macroscopically distinct quantum states with single photon and multiphoton absorption are observed in a strongly driven radio frequency superconducting quantum interference device flux qubit. The amplitude of the resonant peaks and dips are modulated by the power of the applied microwave irradiation and a population inversion is generated at low flux bias. These results, which can be addressed with Landau-Zener transition, are useful to develop an alternative means to initialize and manipulate the flux qubit, as well as to do a controllable population inversion used in a micromaser. © 2009 American Institute of Physics. ͓DOI: 10.1063/1.3093823͔As controllable artificial atoms, superconducting qubits have received considerable attention because of providing a new paradigm of quantum solid state physics. So far, many fantastic macroscopic quantum coherent phenomena 1,2 have been demonstrated in superconducting qubits. In addition, recent experiments show that the interaction between superconducting qubits and microwave ͑MW͒ resonant cavity can produce single photon, 2 which leads to a possible application of superconducting qubits as a micromaser. It is well known that population inversion, which maintains a majority of atoms in excited states rather than in ground state, has to be realized in order to ensure the amplification of the light and thus the laser process. Previous work 3,4 suggests that it is possible to generate population inversion in the superconducting quantum circuits subjected to MW radiation. In this letter, we report a further step in this direction: a controllable population inversion in a strongly driven radio frequency superconducting quantum interference device ͑rf-SQUID͒ by employing Landau-Zener ͑LZ͒ transition.LZ transition is a celebrated quantum mechanical phenomenon in the quantum world.5-7 It has been found in various physical systems, such as atoms in accelerating optical lattices, 8,9 superlattices, 10 nanomagnets, 11,12 quantum dots, 13 and Josephson junctions. [14][15][16] Recently LZ transition is also found in the superconducting qubits, [17][18][19][20] providing new insights into the fundamentals of quantum mechanics and holding promise for the superconducting qubits' application. One may use LZ to enhance the quantum tunneling rate, 21,22 prepare the quantum state, 23 control the qubit gate operations 13,24 effectively, and do the controllable population inversion as demonstrated in this letter.Our design of the superconducting flux qubit, being immune to charge noise and comparatively easy to be read out, is based on rf-SQUID. 25 An rf-SQUID consists of a superconducting loop with inductance L interrupted by one Josephson junction with capacitance C and critical current I c . Its dynamics can be described in terms of the variable ⌽ and are identical to those of a particle of "mass" C with kinetic energy C⌽ 2 / 2 moving in the potential U͑⌽͒. Herewhere ⌽ 0 is the flux quantum,close to one half of a flux quantum is applied, the potential ...

Stark Effect and Generalized Bloch-Siegert Shift in a Strongly Driven Two-Level System

“…We refer to these additional changes in the qubit level splitting as the generalized Bloch-Siegert shift. This work differs from the previous studies on strong drive with superconducting or quantum dot qubits [5,6,[15][16][17][18][19][20][21][22][23][24][25][26], where the coupling of the drive to the qubit was linear.…”

Multiphoton transitions in Josephson-junction qubits (Review Article)

“…Second, the inverse population appears to the right, where the upper level occupation probability P 1 is larger than the ground state probability P 0 , see also Refs. [20,42,144,145] for the study of the population inversion in the systems with single Josephson-junction qubits. These two phenomena are similar to those which exhibit atoms in the laser field [146].…”

“…For strong driving, the width of the resonance lines periodically tends to zero, which can be described as the destructive Landau-Zener-Stückelberg interference [37]. Respective interferograms displayed doubleperiodical dependence of the upper-level occupation probability on the energy bias and the driving amplitude [38][39][40][41][42][43].…”

Amplitude spectroscopy of two coupled qubits

“…In the language of wave functions, an interference of different zone states, predicted by Stückelberg 11 is possible. As applied to qubits these effects have lately been discussed in numerous works [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41] .…”