Time crystals: analysis of experimental conditions

Time crystals are quantum many-body systems which are able to self-organize their motion in a periodic way in time. Discrete time crystals have been experimentally demonstrated in spin systems. However, the first idea of spontaneous breaking of discrete time translation symmetry, in ultra-cold atoms bouncing on an oscillating mirror, still awaits experimental demonstration. Here, we perform a detailed analysis of the experimental conditions needed for the realization of such a discrete time crystal. Importantly, the considered system allows for the realization of dramatic breaking of discrete time translation symmetry where a symmetry broken state evolves with a period tens of times longer than the driving period. Moreover, atoms bouncing on an oscillating mirror constitute a suitable system for the realization of dynamical quantum phase transitions in discrete time crystals and for the demonstration of various non-trivial condensed matter phenomena in the time domain. We show that Anderson localization effects, which are typically associated with spatial disorder and exponential localization of eigenstates of a particle in configuration space, can be observed in the time domain when ultra-cold atoms are bouncing on a randomly moving mirror.Comment: 15 pages, 7 figures, version accepted for publication in Phys. Rev.

Dynamics of reflection of ultracold atoms from a periodic 1D magnetic lattice potential

We report on an experimental study of the dynamics of the reflection of ultracold atoms from a periodic one-dimensional magnetic lattice potential. The magnetic lattice potential of period 10 \textmu m is generated by applying a uniform bias magnetic field to a microfabricated periodic structure on a silicon wafer coated with a multilayered TbGdFeCo/Cr magneto-optical film. The effective thickness of the magnetic film is about 960 nm. A detailed study of the profile of the reflected atoms as a function of externally induced periodic corrugation in the potential is described. The effect of angle of incidence is investigated in detail. The experimental observations are supported by numerical simulations.Comment: 15 pages, 11 figure

Adiabatically induced coherent Josephson oscillations of ultracold atoms in an asymmetric two-dimensional magnetic lattice

We propose a new method to create an asymmetric two-dimensional magnetic lattice which exhibits magnetic band gap structure similar to semiconductor devices. The quantum device is assumed to host bound states of collective excitations formed in a magnetically trapped quantum degenerate gas of ultracold atoms such as a Bose-Einstein condensate (BEC) or a degenerate Fermi gas. A theoretical framework is established to describe possible realization of the exciton-Mott to discharging Josephson states oscillations in which the adiabatically controlled oscillations induce ac and dc Josephson atomic currents where this effect can be used to transfer n Josephson qubits across the asymmetric two-dimensional magnetic lattice. We consider second-quantized Hamiltonians to describe the Mott insulator state and the coherence of multiple tunneling between adjacent magnetic lattice sites where we derive the self consistent non-linear Schrödinger equation with a proper field operator to describe the exciton Mott quantum phase transition via the induced Josephson atomic current across the n magnetic bands

Patterns of symptoms possibly indicative of cancer and associated help-seeking behaviour in a large sample of United Kingdom residents - the USEFUL study

Background.Cancer awareness campaigns aim to increase awareness of the potential seriousness of signs and symptoms of cancer, and encourage their timely presentation to healthcare services. Enhanced understanding of the prevalence of symptoms possibly indicative of cancer in different population subgroups, and associated general practitioner (GP) help-seeking behaviour, will help to target cancer awareness campaigns more effectively.Aim.To determine: i) the prevalence of 21 symptoms possibly indicative of breast, colorectal, lung or upper gastrointestinal cancer in the United Kingdom (UK), including six ‘red flag’ symptoms; ii) whether the prevalence varies among population subgroups; iii) the proportion of symptoms self-reported as presented to GPs; iv) whether GP help-seeking behaviour varies within population subgroups.Methods.Self-completed questionnaire about experience of, and response to, 25 symptoms (including 21 possibly indicative of the four cancers of interest) in the previous month and year; sent to 50,000 adults aged 50 years or more and registered with 21 general practices in Staffordshire, England or across Scotland. Results.Completed questionnaires were received from 16,778 respondents (corrected response rate 34.2%). Almost half (45.8%) of respondents had experienced at least one symptom possibly indicative of cancer in the last month, and 58.5% in the last year. The prevalence of individual symptoms varied widely (e.g. in the last year between near zero% (vomiting up blood) and 15.0% (tired all the time). Red flag symptoms were uncommon. Female gender, inability to work because of illness, smoking, a history of a specified medical diagnosis, low social support and lower household income were consistently associated with experiencing at least one symptom possibly indicative of cancer in both the last month and year. The proportion of people who had contacted their GP about a symptom experienced in the last month varied between 8.1% (persistent cough) and 39.9% (unexplained weight loss); in the last year between 32.8% (hoarseness) and 85.4% (lump in breast). Nearly half of respondents experiencing at least one red flag symptom in the last year did not contact their GP about it. Females, those aged 80+ years, those unable to work because of illness, ex-smokers and those previously diagnosed with a specified condition were more likely to report a symptom possibly indicative of cancer to their GP; and those on high household income less likely.Conclusion.Symptoms possibly indicative of cancer are common among adults aged 50+ years in the UK, although they are not evenly distributed. Help-seeking responses to different symptoms also vary. Our results suggest important opportunities to provide more nuanced messaging and targeting of symptom-based cancer awareness campaigns

Trapping ultracold atoms at 100 nm from a chip surface in a 0.7-micrometer-period magnetic lattice

We report the trapping of ultracold 87Rb atoms in a 0.7 micron-period 2D triangular magnetic lattice on an atom chip. The magnetic lattice is created by a lithographically patterned magnetic Co/Pd multilayer film plus bias fields. Rubidium atoms in the F=1, mF=-1 low-field seeking state are trapped at estimated distances down to about 100 nm from the chip surface and with calculated mean trapping frequencies as high as 800 kHz. The measured lifetimes of the atoms trapped in the magnetic lattice are in the range 0.4 - 1.7 ms, depending on distance from the chip surface. Model calculations suggest the trap lifetimes are currently limited mainly by losses due to surface-induced thermal evaporation following loading of the atoms from the Z-wire trap into the very tight magnetic lattice traps, rather than by fundamental loss processes such as surface interactions, three-body recombination or spin flips due to Johnson magnetic noise. The trapping of atoms in a 0.7 micrometer-period magnetic lattice represents a significant step towards using magnetic lattices for quantum tunneling experiments and to simulate condensed matter and many-body phenomena in nontrivial lattice geometries.Comment: 11 pages, 7 figure

Discrete time crystals in Bose-Einstein Condensates and symmetry-breaking edge in a simple two-mode theory

Discrete time crystals (DTCs) refer to a novel many-body steady state that spontaneously breaks the discrete time-translational symmetry in a periodically-driven quantum system. Here, we study DTCs in a Bose-Einstein condensate (BEC) bouncing resonantly on an oscillating mirror, using a two-mode model derived from a standard quantum field theory. We investigate the validity of this model and apply it to study the long-time behavior of our system. A wide variety of initial states based on two Wannier modes are considered. We find that in previous studies the investigated phenomena in the evolution time-window ($\lessapprox$2000 driving periods) are actually "short-time" transient behavior though DTC formation signaled by the sub-harmonic responses is still shown if the inter-boson interaction is strong enough. After a much longer (about 20 times) evolution time, initial states with no "long-range" correlations relax to a steady state, where time-symmetry breaking can be unambiguously defined. Quantum revivals also eventually occur. This long-time behavior can be understood via the many-body Floquet quasi-eigenenergy spectrum of the two-mode model. A symmetry-breaking edge for DTC formation appears in the spectrum for strong enough interaction, where all quasi-eigenstates below the edge are symmetry-breaking while those above the edge are symmetric. The late-time steady state's time-translational symmetry depends solely on whether the initial energy is above or below the symmetry-breaking edge. A phase diagram showing regions of symmetry-broken and symmetric phases for differing initial energies and interaction strengths is presented. We find that according to this two-mode model, the discrete time crystal survives for times out to at least 250,000 driving periods