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arXiv:cond-mat/0507502 · Europhysics Letters (EPL)

Low-frequency Rabi spectroscopy for a dissipative two-level system

Ya. S Greenberg, E Il'ichev, A Izmalkov

Published Nov 8, 2005• 23 citations
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Abstract

We have analyzed the interaction of a dissipative two-level quantum system with high- and low-frequency excitation. The system is continuously and simultaneously irradiated by these two waves. If the frequency of the first signal is close to the level separation, the response of the system exhibits undamped low-frequency oscillations whose amplitude has a clear resonance at the Rabi frequency with the width being dependent on the damping rates of the system. The method can be useful for low-frequency Rabi spectroscopy in various physical systems which are described by a two-level Hamiltonian, such as nuclei spins in NMR, double-well quantum dots, superconducting flux and charge qubits, etc. As examples, the application of the method to a nuclear spin and to the readout of a flux qubit are briefly discussed.

DOI
10.1209/epl/i2005-10320-y

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We have analyzed the interaction of a dissipative two-level quantum system with high- and low-frequency excitation. The system is continuously and simultaneously irradiated by these two waves. If the frequency of the first signal is close to the level separation, the response of the system exhibits undamped low-frequency oscillations whose amplitude has a clear resonance at the Rabi frequency with the width being dependent on the damping rates of the system. The method can be useful for low-frequency Rabi spectroscopy in various physical systems which are described by a two-level Hamiltonian, such as nuclei spins in NMR, double-well quantum dots, superconducting flux and charge qubits, etc. As examples, the application of the method to a nuclear spin and to the readout of a flux qubit are briefly discussed.
We have analyzed the interaction of a dissipative two level quantum system with high and low frequency excitation. The system is continuously and simultaneously irradiated by these two waves. If the frequency of the first signal is close to the level separation and the second one is tuned to the Rabi frequency, it is shown that the response of the system exhibits an undamped low frequency oscillation. The method can be useful for low frequency Rabi spectroscopy in various physical systems which are described by a two level Hamiltonian, such as nuclei spins in NMR, double well quantum dots, superconducting flux and charge qubits, etc. As an example, the application of the method to the readout of a flux qubit is considered.
We have analyzed a dissipative two-level quantum system (TLS) which is continuously and simultaneously irradiated by high- and low-frequency excitation. The interaction of the TLS with a high-frequency excitation is considered in the frame of the dressed-state approach. A linear response of the coupled TLS and corresponding photon field system to a signal whose frequency is of the order of the Rabi frequency is found. The response exhibits undamped low-frequency oscillations whose amplitude has a clear resonance at the Rabi frequency with the width being dependent on the damping rates of the TLS. The method can be useful for low-frequency Rabi spectroscopy in various physical systems described by a two-level Hamiltonian, such as nuclei spins in NMR, double well quantum dots, superconducting flux, charge qubits, etc. The application of the method to a superconducting flux qubit and to the detection of NMR is considered in detail.
An outstanding challenge in superconducting quantum circuits is mitigating loss from two-level system (TLS) defects. SWAP spectroscopy with flux-tunable qubits can detect individual TLSs, but the Rabi chevrons that signal coherent exchange have been observed only for the most strongly coupled defects. Here, we introduce a sequence with fast flux pulses only at state preparation and readout, switched off during the energy-relaxation delay for finer frequency resolution and longer interaction times. We detect Rabi chevrons at swap rates as low as 0.1 MHz, an order of magnitude lower than previously reported. In the dressed-state picture, we fit the coherent swap oscillations to extract the TLS energy-relaxation time. These Rabi chevrons reveal coherent TLSs with a median energy-relaxation time of 10 microseconds, at coupling strengths previously associated with incoherent TLSs. The swap coherence times exceed the qubit T2* limited by flux noise, indicating that the dressed gap protects them from low-frequency 1/f noise.
We analyze a system composed of a superconducting flux qubit coupled to a transmission-line resonator driven by two signals with frequencies close to the resonator's harmonics. The first strong signal is used for exciting the system to a high energetic state while a second weak signal is applied for probing effective eigenstates of the system. In the framework of doubly dressed states we showed the possibility of amplification and attenuation of the probe signal by direct transitions at the Rabi frequency. We present a brief review of theoretical and experimental works where a direct resonance at Rabi frequency have been investigated in superconducting flux qubits. The interaction of the qubit with photons of two harmonics has prospects to be used as a quantum amplifier (microwave laser) or an attenuator.
Understanding the nature of two-level tunneling defects is important for minimizing their disruptive effects in various nanodevices. By exploiting the resonant coupling of these defects to a superconducting qubit, one can probe and coherently manipulate them individually. In this work, we utilize a phase qubit to induce Rabi oscillations of single tunneling defects and measure their dephasing rates as a function of the defect's asymmetry energy, which is tuned by an applied strain. The dephasing rates scale quadratically with the external strain and are inversely proportional to the Rabi frequency. These results are analyzed and explained within a model of interacting defects, in which pure dephasing of coherent high-frequency (gigahertz) defects is caused by interaction with incoherent low-frequency thermally excited defects. Our analysis sets an upper bound for the relaxation rates of thermally excited defects interacting strongly with strain fields.
The properties of a superconducting flux quantum bit (qubit) in the quasidispersive mode, where the frequency of a probe signal is lower than the qubit excitation frequency but is close to it, have been experimentally studied. It has been shown that all parameters of the qubit inductively coupled to a coplanar resonator can be determined at the single-frequency excitation from the analysis of the frequency responses of the transmission of the probe signal at the output of this resonator. Under the additional excitation of the qubit by the signal at the second harmonic of the cavity, resonance dips have been observed because of resonance between the probe signal and induced Rabi splitting. It has been shown that the positions of these dips are in good agreement with the parameters of the qubit that are obtained by analyzing the amplitude–frequency response within the width of the fundamental resonance frequency.