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arXiv:cond-mat/0609144 · Physical Review B

Low-frequency Rabi spectroscopy of dissipative two-level systems: Dressed-state approach

Ya. S. Greenberg

Published Sep 26, 2007• 36 citations
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Abstract

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.

DOI
10.1103/physrevb.76.104520

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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.
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.
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 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 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.
The dynamics of a two-level spin system dressed by bichromatic radiation is studied under the conditions of double resonance when the frequency of one (microwave) field is equal to the Larmor frequency of the spin system and the frequency of the other (radio-frequency) field ω rf is close to the Rabi frequency ω 1 in a microwave field. It is shown theoretically that Rabi oscillations between dressed-spin states with the frequency ɛ are accompanied by higher-frequency oscillations at frequencies n ω rf and n ω rf ± ɛ, where n = 1, 2,.... The most intense among these are the signals corresponding to n = 1. The counter-rotating (antiresonance) components of the RF field give rise to a shift of the dressed-state energy, i.e., to a frequency shift similar to the Bloch-Siegert shift. In particular, this shift is manifested as the dependence of the Rabi-oscillation frequency ɛ on the sign of the detuning ω 1 − ω rf from resonance. In the case of double resonance, the oscillation amplitude is asymmetric; i.e., the amplitude at the sum frequency ω rf + ɛ increases, while the amplitude at the difference frequency ω rf − ɛ decreases. The predicted effects are confirmed by observations of the nutation signals of the electron paramagnetic resonance (EPR) of E ′ 1 centers in quartz and should be taken into account to realize qubits with a low Rabi frequency in solids.
We use the density matrix formalism to analyze the interaction of interferometer-type superconducting qubits with a high quality tank circuit, which frequency is well below the gap frequency of a qubit. We start with the ground state characterization of the superconducting flux and charge qubits. Then, by making use of a dressed state approach, we describe the qubits' spectroscopy when the qubit is irradiated by a microwave field which is tuned to the gap frequency. The last section of the paper is devoted to continuous monitoring of qubit states by using a dc superconducting quantum interference device in the inductive mode.