Measuring a topological transition in an artificial spin- 1/2 system

Physical Review Letters

Volumn 113, Issue 5, 2014, Pages

  Schroer, M D ^a   Kolodrubetz, M H ^b   Kindel, W F ^a   Sandberg, M ^c   Gao, J ^c   Vissers, M R ^c   Pappas, D P ^c   Polkovnikov, Anatoli ^b   Lehnert, K W ^a  

^a UNIVERSITY OF COLORADO   (United States)

^b Boston University   (United States)

^c NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

QUANTUM COMPUTERS; TOPOLOGY;

CHERN NUMBERS; MEASUREMENTS OF; NON-ADIABATIC RESPONSE; SUPERCONDUCTING QUBITS; TOPOLOGICAL PROPERTIES; TOPOLOGICAL TRANSITIONS; TWO-LEVEL SYSTEM;

HAMILTONIANS;

EID: 84905572190     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.113.050402     Document Type: Article

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42. We note that the qubit is initialized in its bare ground state ((Equation presented)), and for technical reasons, we ramp (Equation presented) from positive to negative values. This is formally the excited state of Eq. (4) at (Equation presented), although the distinction between ground and excited states is arbitrary for periodically driven Hamiltonians in the Floquet picture [49]. Our method works for arbitrary eigenstates of the initial Hamiltonian, so the particular state targeted is irrelevant.
43. We note that a more microscopic view of the dephasing has been obtained in similar systems using the Bloch-Redfield equations [45]. While the results are quantitatively different, our relaxation and dephasing are small; hence, the difference between Bloch-Redfield and Lindbladian dynamics should be minimal.
44. The fit was performed with only one free parameter, an effective offset field (Equation presented), to account for an unexpected shift in the frequency of the qubit, which we attributed to a weak Stark shift.
45. This approximation is justified for a two-level system as (Equation presented), where (Equation presented) and (Equation presented) are ground and excited state wave functions.
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