14 research outputs found
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