Quantum Control of Ultra-cold Atoms: Uncovering a Novel Connection between Two Paradigms of Quantum Nonlinear Dynamics

Controlling the translational motion of cold atoms using optical lattice potentials is of both theoretical and experimental interest. By designing two on-resonance time sequences of kicking optical lattice potentials, a novel connection between two paradigms of nonlinear mapping systems, i.e., the kicked rotor model and the kicked Harper model, is established. In particular, it is shown that Hofstadter's butterfly quasi-energy spectrum in periodically driven quantum systems may soon be realized experimentally, with the effective Planck constant tunable by varying the time delay between two sequences of control fields. Extensions of this study are also discussed. The results are intended to open up a new generation of cold-atom experiments of quantum nonlinear dynamicsComment: submitted to the special issue of "Quantum Control of Matter and Light", Journal of Modern Optic

Quantum state tomography of molecular rotation

We show how the rotational quantum state of a linear or symmetric top rotor can be reconstructed from finite time observations of the polar angular distribution under certain conditions. The presented tomographic method can reconstruct the complete rotational quantum state in many non-adiabatic alignment experiments. Our analysis applies for measurement data available with existing measurement techniques.Comment: 7 pages, 1 figur

Tomographic reconstruction of quantum correlations in excited Bose-Einstein condensates

We propose to use quantum tomography to characterize the state of a perturbed Bose-Einstein condensate. We assume knowledge of the number of particles in the zero-wave number mode and of density distributions in space at different times, and we treat the condensate in the Bogoliubov approximation. For states that can be treated with the Gross-Pitaevskii equation, we find that the reconstructed density operator gives excellent predictions of the second moments of the atomic creation- and annihilation operators, including the one-body density matrix. Additional inclusion of the momentum distribution at one point of time enables somewhat reliable predictions to be made for the second moments for mixed states, making it possible to distinguish between coherent and thermal perturbations of the condensate. Finally, we find that with observation of the zero-wave number mode's anomalous second moment the reconstructed density operator gives reliable predictions of the second moments of locally amplitude squeezed states.Comment: 12 pages, 7 figure

Tomographic reconstruction of quantum states in N spatial dimensions

Most quantum tomographic methods can only be used for one-dimensional problems. We show how to infer the quantum state of a non-relativistic N-dimensional harmonic oscillator system by simple inverse Radon transforms. The procedure is equally applicable to finding the joint quantum state of several distinguishable particles in different harmonic oscillator potentials. A requirement of the procedure is that the angular frequencies of the N harmonic potentials are incommensurable. We discuss what kind of information can be found if the requirement of incommensurability is not fulfilled and also under what conditions the state can be reconstructed from finite time measurements. As a further example of quantum state reconstruction in N dimensions we consider the two related cases of an N-dimensional free particle with periodic boundary conditions and a particle in an N-dimensional box, where we find a similar condition of incommensurability and finite recurrence time for the one-dimensional system.Comment: 8 pages, 1 figur

Spectral Relationships Between Kicked Harper and On-Resonance Double Kicked Rotor Operators

Kicked Harper operators and on-resonance double kicked rotor operators model quantum systems whose semiclassical limits exhibit chaotic dynamics. Recent computational studies indicate a striking resemblance between the spectrums of these operators. In this paper we apply C*-algebra methods to explain this resemblance. We show that each pair of corresponding operators belong to a common rotation C*-algebra B_\alpha, prove that their spectrums are equal if \alpha is irrational, and prove that the Hausdorff distance between their spectrums converges to zero as q increases if \alpha = p/q with p and q coprime integers. Moreover, we show that corresponding operators in B_\alpha are homomorphic images of mother operators in the universal rotation C*-algebra A_\alpha that are unitarily equivalent and hence have identical spectrums. These results extend analogous results for almost Mathieu operators. We also utilize the C*-algebraic framework to develop efficient algorithms to compute the spectrums of these mother operators for rational \alpha and present preliminary numerical results that support the conjecture that their spectrums are Cantor sets if \alpha is irrational. This conjecture for almost Mathieu operators, called the Ten Martini Problem, was recently proved after intensive efforts over several decades. This proof for the almost Mathieu operators utilized transfer matrix methods, which do not exist for the kicked operators. We outline a strategy, based on a special property of loop groups of semisimple Lie groups, to prove this conjecture for the kicked operators.Comment: 26 pages, 8 figure

Nationwide Survival Benefit after Implementation of First-Line Immunotherapy for Patients with Advanced NSCLC—Real World Efficacy

SIMPLE SUMMARY: The expected change in overall survival (OS) in patients with advanced non-small cell lung cancer (NSCLC) after the clinical implementation of immune checkpoint inhibitor therapy (ICI) has not been substantially investigated in large real-world cohorts outside randomized controlled trials (RCTs). In this nationwide study, we compared OS before and after the implementation of ICI and found that 3-year OS tripled from 6% to 18%. Patients receiving ICI had a lower OS than demonstrated in RCTs, except for patients with performance status (PS) 0. More than a fifth of the patients progressed early within the first six ICI cycles. Adverse prognostic factors were PS ≥ 1 and metastases to the bone and liver. ABSTRACT: Background The selection of patients with non-small cell lung cancer (NSCLC) for immune checkpoint inhibitor (ICI) treatment remains challenging. This real-world study aimed to compare the overall survival (OS) before and after the implementation of ICIs, to identify OS prognostic factors, and to assess treatment data in first-line (1L) ICI-treated patients without epidermal growth factor receptor mutation or anaplastic lymphoma kinase translocation. Methods Data from the Danish NSCLC population initiated with 1L palliative antineoplastic treatment from 1 January 2013 to 1 October 2018, were extracted from the Danish Lung Cancer Registry (DLCR). Long-term survival and median OS pre- and post-approval of 1L ICI were compared. From electronic health records, additional clinical and treatment data were obtained for ICI-treated patients from 1 March 2017 to 1 October 2018. Results The OS was significantly improved in the DLCR post-approval cohort (n = 2055) compared to the pre-approval cohort (n = 1658). The 3-year OS rates were 18% (95% CI 15.6–20.0) and 6% (95% CI 5.1–7.4), respectively. On multivariable Cox regression, bone (HR = 1.63) and liver metastases (HR = 1.47), performance status (PS) 1 (HR = 1.86), and PS ≥ 2 (HR = 2.19) were significantly associated with poor OS in ICI-treated patients. Conclusion OS significantly improved in patients with advanced NSCLC after ICI implementation in Denmark. In ICI-treated patients, PS ≥ 1, and bone and liver metastases were associated with a worse prognosis