Emission spectrum of the driven nonlinear oscillator

Motivated by recent "circuit QED" experiments we investigate the noise properties of coherently driven nonlinear resonators. By using Josephson junctions in superconducting circuits, strong nonlinearities can be engineered, which lead to the appearance of pronounced effects already for a low number of photons in the resonator. Based on a master equation approach we determine the emission spectrum and observe for typical circuit QED parameters, in addition to the primary Raman-type peaks, second-order peaks. These peaks describe higher harmonics in the slow noise-induced fluctuations of the oscillation amplitude of the resonator and provide a clear signature of the nonlinear nature of the system.Comment: 8 pages, 5 figure

Phase diffusion and locking in single-qubit lasers

Motivated by recent experiments, which demonstrated lasing and cooling of the electromagnetic field in an electrical resonator coupled to a superconducting qubit, we study the phase coherence and diffusion of the system in the lasing state. We also discuss phase locking and synchronization induced by an additional {\sl ac} driving of the resonator. We extend earlier work to account for the strong qubit-resonator coupling and to include the effects of low-frequency qubit's noise. We show that the strong coupling may lead to a double peak structure of the spectrum, while the shape and width are determined to the low-frequency noise.Comment: Revised version with a new section about the validity of the model when applied to describe experiment

Interpersonal Change During Inpatient CBASP Treatment: Focus on Group Therapy

Background: The Cognitive Behavioral Analysis System of Psychotherapy (CBASP) has been tailored specifically to the demands of patients with persistent depressive disorder (PDD). According to the CBASP model, PDD patients are supposed to live perceptually disconnected from their social environment, which consequently maintains depression. While initially developed as an individual treatment modality, the adaptation for group therapy yields an important interpersonal space. However, little is known about the specific factors that contribute to patients' benefit from the CBASP group modality. Methods: The analyzed sample comprised N = 87 PDD patients who completed a 12 week multimodal inpatient treatment including 2 weekly CBASP-specific individual and group sessions, respectively, as well as CBASP-unspecific medical contacts, pharmacotherapy and complementary therapies. Group sessions included trainings in situational analysis and interpersonal skills. Interpersonal change over therapy was examined based on the patients' self-perceived interpersonal problems (IIP) and the impact messages as perceived by their individual therapists (IMI). Pre and post-treatment data were compared using within-sample t-tests. Additionally, patients evaluated CBASP group therapy on a feedback form. They were invited to reflect on individual benefits and its helpful and unhelpful aspects. Qualitative content analysis with inductive category development was used to analyze feedback. Inter-rater reliability was computed to confirm categories before summarizing the frequencies of reported factors. Results: Self-perceived interpersonal distress significantly decreased over therapy. Patients reported reduced interpersonal problems and therapists reported more friendly and dominant impact messages. Interestingly, patients who showed a significant depressive symptom reduction described higher change scores. Regarding qualitative data, patients reported five main benefits from group therapy: Gain in social competence, self-confidence, self-reflection, interpersonal dynamics, and optimism/universality. Patients responding to CBASP identified significantly more factors than non-responders. Conclusions: Compared to studies with individual CBASP only, the present findings suggest that CBASP group therapy may contribute to the improvement of interpersonal behavior. Group therapy is discussed as a potential boosting effect for individual CBASP. However, as the present data were collected in a multimodal inpatient setting without competitor, randomized controlled trials are warranted that investigate the specific benefits of the group modality or the combined individual and group therapy over individual CBASP only

The role of damping for the driven anharmonic quantum oscillator

For the model of a linearly driven quantum anharmonic oscillator, the role of damping is investigated. We compare the position of the stable points in phase space obtained from a classical analysis to the result of a quantum mechanical analysis. The solution of the full master equation shows that the stable points behave qualitatively similar to the classical solution but with small modifications. Both the quantum effects and additional effects of temperature can be described by renormalizing the damping.Comment: 4 pages, 2 figures; submitted to "Journal of Physics: Conference Series

Few-Qubit lasing in circuit QED

Motivated by recent experiments, which demonstrated lasing and cooling of the electromagnetic modes in a resonator coupled to a superconducting qubit, we describe the specific mechanisms creating the population inversion, and we study the spectral properties of these systems in the lasing state. Different levels of the theoretical description, i.e., the semi-classical and the semi-quantum approximation, as well as an analysis based on the full Liouville equation are compared. We extend the usual quantum optics description to account for strong qubit-resonator coupling and include the effects of low-frequency noise. Beyond the lasing transition we find for a single- or few-qubit system the phase diffusion strength to grow with the coupling strength, which in turn deteriorates the lasing state.Comment: Prepared for the proceedings of the Nobel Symposium 2009, Qubits for future quantum computers, May 2009 in Goeteborg, Sweden. Published versio

Single-qubit lasing in the strong-coupling regime

Motivated by recent ``circuit QED'' experiments we study the lasing transition and spectral properties of single-qubit lasers. In the strong coupling, low-temperature regime quantum fluctuations dominate over thermal noise and strongly influence the linewidth of the laser. When the qubit and the resonator are detuned, amplitude and phase fluctuations of the radiation field are coupled, and the phase diffusion model, commonly used to describe conventional lasers, fails. We predict pronounced effects near the lasing transition, with an enhanced linewidth and non-exponential decay of the correlation functions. We cover a wide range of parameters by using two complementary approaches, one based on the Liouville equation in a Fock state basis, covering arbitrarily strong coupling but limited to low photon numbers, the other based on the coherent-state representation, covering large photon numbers but restricted to weak or intermediate coupling.Comment: 11 pages, 11 figure

Dissipation in circuit quantum electrodynamics: lasing and cooling of a low-frequency oscillator

Superconducting qubits coupled to electric or nanomechanical resonators display effects previously studied in quantum electrodynamics (QED) and extensions thereof. Here we study a driven qubit coupled to a low-frequency tank circuit with particular emphasis on the role of dissipation. When the qubit is driven to perform Rabi oscillations, with Rabi frequency in resonance with the oscillator, the latter can be driven far from equilibrium. Blue detuned driving leads to a population inversion in the qubit and lasing behavior of the oscillator ("single-atom laser"). For red detuning the qubit cools the oscillator. This behavior persists at the symmetry point where the qubit-oscillator coupling is quadratic and decoherence effects are minimized. Here the system realizes a "single-atom-two-photon laser".Comment: 9 pages, written for the Focus Issue of New J. Phys. on "Mechanical Systems at the Quantum Limit", ed. by Markus Aspelmeyer and Keith Schwa

Comparison of different methods for post-therapeutic dosimetry in [177Lu]Lu-PSMA-617 radioligand therapy

Background Dosimetry is of high importance for optimization of patient-individual PSMA-targeted radioligand therapy (PSMA-RLT). The aim of our study was to evaluate and compare the feasibility of different approaches of image-based absorbed dose estimation in terms of accuracy and effort in clinical routine. Methods Whole-body planar images and SPECT/CT images were acquired from 24 patients and 65 cycles at 24h, 48h, and ≥96h after administration of a mean activity of 6.4 GBq [177Lu]Lu-PSMA-617 (range 3–10.9 GBq). Dosimetry was performed by use of the following approaches: 2D planar-based dosimetry, 3D SPECT/CT-based dosimetry, and hybrid dosimetry combining 2D and 3D data. Absorbed doses were calculated according to IDAC 2.1 for the kidneys, the liver, the salivary glands, and bone metastases. Results Mean absorbed doses estimated by 3D dosimetry (the reference method) were 0.54 ± 0.28 Gy/GBq for the kidneys, 0.10 ± 0.05 Gy/GBq for the liver, 0.81 ± 0.34 Gy/GBq for the parotid gland, 0.72 ± 0.39 Gy/GBq for the submandibular gland, and 1.68 ± 1.32 Gy/GBq for bone metastases. Absorbed doses of normal organs estimated by hybrid dosimetry showed small, non-significant differences (median up to 4.0%) to the results of 3D dosimetry. Using 2D dosimetry, in contrast, significant differences (median up to 10.9%) were observed. Regarding bone metastases, small, but significant differences (median up to 7.0%) of absorbed dose were found for both, 2D dosimetry and hybrid dosimetry. Bland-Altman analysis revealed high agreement between hybrid dosimetry and 3D dosimetry for normal organs and bone metastases, but substantial differences between 2D dosimetry and 3D dosimetry. Conclusion Hybrid dosimetry provides high accuracy in estimation of absorbed dose in comparison to 3D dosimetry for all important organs and is therefore feasible for use in individualized PSMA-RLT