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When a system's parameter is abruptly changed, a relaxation towards the new equilibrium of the system follows. We show that a crossing between the second and third eigenvalues of the relaxation matrix results in a relaxation trajectory singularity, which is analogous to a first-order equilibrium phase transition. We demonstrate this in a minimal 4-state system and in the thermodynamic limit of the 1D Ising model.

Recently, there has been growing interest in the utilization of physical systems as heuristic optimizers for classical spin Hamiltonians. A prominent approach employs gain-dissipative optical oscillator networks for this purpose. Unfortunately, these systems inherently suffer from an inexact mapping between the oscillator network loss rate and the spin Hamiltonian due to additional degrees of freedom present in the system such as oscillation amplitude. In this work, we theoretically analyze and experimentally demonstrate a scheme for the alleviation of this difficulty. The scheme involves control over the laser oscillator amplitude through modification of individual laser oscillator loss. We demonstrate this approach in a laser network classical XY model simulator based on a digital degenerate cavity laser. We prove that for each XY model energy minimum there corresponds a unique set of laser loss values that leads to a network state with identical oscillation amplitudes and to phase values that coincide with the XY model minimum. We experimentally demonstrate an eight fold improvement in the deviation from the minimal XY energy by employing our proposed solution scheme.

Phase transitions are emergent phenomena where microscopic interactions drive a disordered system into a collectively ordered phase. Near the boundary between two phases, the system can exhibit critical, scale-invariant behavior. Here, we report on a second-order phase transition accompanied by critical behavior in a system of warm cesium spins driven by linearly-polarized light. The ordered phase exhibits macroscopic magnetization when the interactions between the spins become dominant. We measure the phase diagram of the system and observe the collective behavior near the phase boundaries, including power-law dependence of the magnetization and divergence of the susceptibility. Out of equilibrium, we observe a critical slow-down of the spin response time by two orders of magnitude, exceeding five seconds near the phase boundary. This work establishes a controlled platform for investigating equilibrium and nonequilibrium properties of magnetic phases., Y.H. and O.K. contributed equally

We demonstrate experimentally and validate theoretically an exact mapping between coupled-lasers networks and classical spin Hamiltonians by adjusting the loss rate of the individual lasers.

Non-Hermitian Hamiltonians, and particularly parity-time (PT) and anti-PT symmetric Hamiltonians, play an important role in many branches of physics, from quantum mechanics to optical systems and acoustics. Both the PT and anti-PT symmetries are specific instances of a broader class known as anyonic-PT symmetry, where the Hamiltonian and the PT operator satisfy a generalized commutation relation. Here, we study theoretically these novel symmetries and demonstrate them experimentally in coupled lasers systems. We resort to complex coupling of mixed dispersive and dissipative nature, which allows unprecedented control on the location in parameter space where the symmetry and symmetry breaking occur. Moreover, tuning the coupling in the same physical system allows us to realize the special cases of PT and anti-PT symmetries. In a more general perspective, we present and experimentally validate a new relation between laser synchronization and the symmetry of the underlying non-Hermitian Hamiltonian.

Computations implemented on a physical system are fundamentally limited by the laws of physics. A prominent example for a physical law that bounds computations is the Landauer principle. According to this principle, erasing a bit of information requires a concentration of probability in phase space, which by Liouville's theorem is impossible in pure Hamiltonian dynamics. It therefore requires dissipative dynamics with heat dissipation of at least $k_BT\log 2$ per erasure of one bit. Using a concrete example, we show that when the dynamic is confined to a single energy shell it is possible to concentrate the probability on this shell using Hamiltonian dynamic, and therefore to implement an erasable bit with no thermodynamic cost., 3 Figures, 14 pages

The Landauer’s principle sets a thermodynamic bound of kBT ln 2 on the energetic cost of erasing each bit of information. It holds for any memory device, regardless of its physical implementation. It was recently shown that carefully built artificial devices can saturate this bound. In contrast, biological computation-like processes, e.g., DNA replication, transcription and translation use an order of magnitude more than their Landauer’s minimum. Here we show that saturating the Landauer bound is nevertheless possible with biological devices. This is done using a mechanosensitive channel of small conductance (MscS) from E. coli as a memory bit. MscS is a fast-acting osmolyte release valve adjusting turgor pressure inside the cell. Our patch-clamp experiments and data analysis demonstrate that under a slow switching regime, the heat dissipation in the course of tension-driven gating transitions in MscS closely approaches its Landauer’s limit. We discuss the biological implications of this physical trait.

Skin cancer, including both melanoma and non-melanoma, is the most common type of malignancy, which causes substantial morbidities and mortalities. Although the significant increase in the understanding of skin cancer formation and the development of novel personalized drug regimens have occurred, new treatment options are always of need. The use of natural compounds to alleviate the symptoms or even to prevent and treat cancer has long been proposed. Specifically, the use of marine-based organisms as a source for cancer cure and remedy is being evaluated extensively. The objective of the current study was to assess the ability of the green microalgae Dunaliella salina, the Dead-Sea-derived Haloferax volcanii, and its combinations to treat skin cancer in vitro. The results demonstrate the Dunaliella and Haloferax can reduce sarcoma and basal cell carcinoma cellular growth. Importantly, their combination acts synergistically in a caspase-3 independent manner. Moreover, a synergistic action was found when evaluated sarcoma cell invasion rate, which was completely blocked at pharmacological relevant amounts of the compounds. Collectively, the results demonstrate that the combination of Haloferax volcanii and Dunaliella salina can be used as a new treatment for skin cancer. The specific mechanism of action and further in vivo validation studies are of need.

Under certain conditions, it takes a shorter time to cool a hot system than to cool the same system initiated at a lower temperature. This phenomenon-the "Mpemba effect"-was first observed in water and has recently been reported in other systems. Whereas several detail-dependent explanations were suggested for some of these observations, no common underlying mechanism is known. Using the theoretical framework of nonequilibrium thermodynamics, we present a widely applicable mechanism for a similar effect, the Markovian Mpemba effect, derive a sufficient condition for its appearance, and demonstrate it explicitly in three paradigmatic systems: the Ising model, diffusion dynamics, and a three-state system. In addition, we predict an inverse Markovian Mpemba effect in heating: Under proper conditions, a cold system can heat up faster than the same system initiated at a higher temperature. We numerically demonstrate that this inverse effect is expected in a 1D antiferromagnet nearest-neighbors interacting Ising chain in the presence of an external magnetic field. Our results shed light on the mechanism behind anomalous heating and cooling and suggest that it should be possible to observe these in a variety of systems.

What is the fastest way to heat a system which is coupled to a temperature controlled oven? The intuitive answer is to use only the hottest temperature available. However, we show that often it is possible to achieve an exponentially faster heating, and propose a strategy to find the optimal protocol. Surprisingly, this protocol can have a pre-cooling stage -- cooling the system before heating it shortens the heating time significantly. This approach can be applied to many-body systems, as we demonstrate in the 2D antiferromagnet Ising model., Supp. Info. is attached as a separated file

Bacterial mechanosensitive channels are major players in cells’ ability to cope with hypo-osmotic stress. Excess turgor pressure due to fast water influx is reduced as the channels, triggered by membrane tension, open and release osmolytes. However,in vitromeasurements of the free energy difference between the open and closed states of ion channels are challenging due to hysteresis effects and inactivation. Exploiting recent developments in statistical physics, we present a general formalism to extract the free energy difference between the closed and open states of mechanosensitive ion channels from non-equilibrium work distributions associated with the channels’ gating recorded in native patches under ramp stimulation protocols. We show that the work distributions obtained from the gating of MscS channels inE. colimembrane satisfy the strong symmetry relations predicted by the fluctuation theorems and recover the equilibrium free energy difference between the closed and open states of the channel within 1 kBT of its best estimate obtained from an independent experiment.

Nature photonics 13(2), 91 - 95 (2019). doi:10.1038/s41566-018-0308-z, A key challenge in attosecond science is the temporal characterization of attosecond pulses that are essential for understanding the evolution of electronic wavefunctions in atoms, molecules and solids. Current characterization methods, based on nonlinear light–matter interactions, are limited in terms of stability and waveform complexity. Here, we experimentally demonstrate a conceptually new linear and all-optical pulse characterization method, inspired by double-blind holography. Holography is realized by measuring the extreme ultraviolet (XUV) spectra of two unknown attosecond signals and their interference. Assuming a finite pulse duration constraint, we reconstruct the missing spectral phases and characterize the unknown signals in both isolated pulse and double pulse scenarios. This method can be implemented in a wide range of experimental realizations, enabling the study of complex electron dynamics via a single-shot and linear measurement., Published by Nature Publ. Group, London [u.a.]

A system that violates detailed balance evolves asymptotically into a nonequilibrium steady state with non-vanishing currents. Analogously, when detailed balance holds at any instant of time but the system is driven through time-periodic variations of external parameters, it evolves toward a time-periodic state, which can also support non-vanishing currents. In both cases the maintenance of currents throughout the system incurs a cost in terms of entropy production. Here we compare these two scenarios for one dimensional diffusive systems with periodic boundary condition, a framework commonly used to model biological and artificial molecular machines. We first show that the entropy production rate in a periodically driven system is necessarily greater than that in a stationary system without detailed balance, when both are described by the same (time-averaged) current and probability distribution. Next, we show how to construct both a non-equilibrium steady state and a periodic driving that support a given time averaged probability distribution and current. Lastly, we show that although the entropy production rate of a periodically driven system is higher than that of an equivalent steady state, the difference between the two entropy production rates can be tuned to be arbitrarily small.

The Mpemba effect is a counter-intuitive relaxation phenomenon, where a system prepared at a hot temperature cools down faster than an identical system initiated at a cold temperature when both are quenched to an even colder bath. Such non-monotonic relaxations were observed in various systems, including water, magnetic alloys, polymers, and driven granular gases. We analyze the Mpemba effect in Markovian dynamics and discover that a stronger version of the effect often exists for a carefully chosen set of initial temperatures. In this \emph{strong Mpemba effect}, the relaxation time jumps to a smaller value leading to exponentially faster equilibration dynamics. The number of such special initial temperatures defines the \emph{Mpemba index}, whose parity is a topological property of the system. To demonstrate these concepts, we first analyze the different types of Mpemba relaxations in the mean field anti-ferromagnet Ising model, which demonstrates a surprisingly rich Mpemba phase diagram. Moreover, we show that the strong effect survives the thermodynamic limit and that it is tightly connected with thermal overshoot -- in the relaxation process, the temperature of the relaxing system can decay non-monotonically as a function of time. Using the parity of the Mpemba index, we then study the occurrence of the strong Mpemba effect in a large class of thermal quench processes and show that it happens with non-zero probability even in the thermodynamic limit. This is done by introducing the \emph{isotropic} model for which we obtain analytical lower bound estimates for the probability of the strong Mpemba effects. Consequently, we expect that such exponentially faster relaxations can be observed experimentally in a wide variety of systems.

The waveforms of attosecond pulses produced by high-harmonic generation carry information on the electronic structure and dynamics in atomic and molecular systems. Current methods for the temporal characterization of such pulses have limited sensitivity and impose significant experimental complexity. We propose a new linear and all-optical method inspired by widely-used multi-dimensional phase retrieval algorithms. Our new scheme is based on the spectral measurement of two attosecond sources and their interference. As an example, we focus on the case of spectral polarization measurements of attosecond pulses, relying on their most fundamental property -- being well confined in time. We demonstrate this method numerically reconstructing the temporal profiles of attosecond pulses generated from aligned $CO_2$ molecules., Comment: 4 pages 3 figures

Under static conditions, a system satisfying detailed balance generically relaxes to an equilibrium state in which there are no currents. To generate persistent currents, either detailed balance must be broken or the system must be driven in a time-dependent manner. A stationary system that violates detailed balance evolves to a nonequilibrium steady state (NESS) characterized by fixed currents. Conversely, a system that satisfies instantaneous detailed balance but is driven by the time-periodic variation of external parameters—also known as a stochastic pump (SP)—reaches a periodic state with nonvanishing currents. In both cases, these currents are maintained at the cost of entropy production. Are these two paradigmatic scenarios effectively equivalent? For discrete-state systems, we establish a mapping between nonequilibrium stationary states and stochastic pumps. Given a NESS characterized by a particular set of stationary probabilities, currents, and entropy production rates, we show how to construct a SP with exactly the same (time-averaged) values. The mapping works in the opposite direction as well. These results establish a proof of principle: They show that stochastic pumps are able to mimic the behavior of nonequilibrium steady states, and vice versa, within the theoretical framework of discrete-state stochastic thermodynamics. Nonequilibrium steady states and stochastic pumps are often used to model, respectively, biomolecular motors driven by chemical reactions and artificial molecular machines steered by the variation of external, macroscopic parameters. Our results loosely suggest that anything a biomolecular machine can do, an artificial molecular machine can do equally well. We illustrate this principle by showing that kinetic proofreading, a NESS mechanism that explains the low error rates in biochemical reactions, can be effectively mimicked by a constrained periodic driving.

The phase retrieval problem arises in various fields ranging from physics and astronomy to biology and microscopy. Computational reconstruction of the Fourier phase from a single diffraction pattern is typically achieved using iterative alternating projections algorithms imposing a non-convex computational challenge. A different approach is holography, relying on a known reference field. Here we present a conceptually new approach for the reconstruction of two (or more) sufficiently separated objects. In our approach we combine the constraint the objects are finite as well as the information in the interference between them to construct an overdetermined set of linear equations. We show that this set of equations is guaranteed to yield the correct solution almost always and that it can be solved efficiently by standard numerical algebra tools. Essentially, our method combine commonly used constraint (that the object is finite) with a holographic approach (interference information). It differs from holographic methods in the fact that a known reference field is not required, instead the unknown objects serve as reference to one another (hence blind holography). Our method can be applied in a single-shot for two (or more) separated objects or with several measurements with a single object. It can benefit phase imaging techniques such as Fourier phytography microscopy, as well as coherent diffractive X-ray imaging in which the generation of a well-characterized, high resolution reference beam imposes a major challenge. We demonstrate our method experimentally both in the optical domain and in the X-ray domain using XFEL pulses.

Thermodynamics places a limit on the efficiency of heat engines, but not on their output power or on how the power and efficiency change with the engine's cycle time. In this manuscript, we develop a geometrical description of the power and efficiency as a function of the cycle time, applicable to an important class of heat engine models. This geometrical description is used to design engine protocols that attain both the maximal power and maximal efficiency at the fast driving limit. Furthermore, using this method we also prove that no protocol can exactly attain the Carnot efficiency at non-zero power.

In this paper we consider the following real-valued and finite dimensional specific instance of the 1-D classical phase retrieval problem. Let ${\bf F}\in\mathbb{R}^N$ be an $N$-dimensional vector, whose discrete Fourier transform has a compact support. The sign problem is to recover ${\bf F}$ from its magnitude $|{\bf F}|$. First, in contrast to the classical 1-D phase problem which in general has multiple solutions, we prove that with sufficient over-sampling, the sign problem admits a unique solution. Next, we show that the sign problem can be viewed as a special case of a more general piecewise constant phase problem. Relying on this result, we derive a computationally efficient and robust to noise sign recovery algorithm. In the noise-free case and with a sufficiently high sampling rate, our algorithm is guaranteed to recover the true sign pattern. Finally, we present two phase retrieval applications of the sign problem: (i) vectorial phase retrieval with three measurement vectors; and (ii) recovery of two well separated 1-D objects., Comment: 23 pages

Short-pulse lasers allow the most accurate measurement of fast phenomena such as the dynamics of atoms and even electrons. Unfortunately, pulses in the visible region of the spectrum cannot be shorter than the period of one optical cycle: a couple of femtoseconds (one femtosecond is a millionth of a billionth of a second). However, this limit can be overcome when the laser field is very strong, so that its interaction with matter becomes extremely nonlinear, enabling one to zoom in and initiate processes that evolve during a fraction of an optical cycle [1]. This breakthrough, known as high-harmonic generation or HHG, lets researchers produce electromagnetic pulses with durations of attoseconds (thousandths of a femtosecond) and wavelengths in the extreme-ultraviolet or x-ray regime. In Physical Review X, a collaboration lead by Andrius Baltuska of the Technical University of Vienna, Austria, demonstrates an important advance in HHG, showing that carefully chosen combinations of three synchronized optical beams can produce higher frequencies and photon flux [2]. Controlling the generation of these pulses is essential for the observation and manipulation of extremely fast phenomena, such as multielectron processes.

We will present how large array of coupled laser can solves complicated mathematical problems, such as phase retrieval of X-ray imaging experiments, in a microsecond instead of days or even weeks in cluster of powerful computers.

We experimentally demonstrate first-order (fold) and second-order (cusp) catastrophes in the density of an atomic cloud reflected from an optical barrier in the presence of gravity, and show their corresponding universal asymptotic behavior. The cusp point enables robust, field-free refocusing of an expanding atomic cloud with a wide velocity distribution. Specifically, the density attained at the cusp point in our experiment reached 65% of the peak density of the atoms in the trap prior to their release. We thereby add caustics to the various phenomena with parallels in optics that can be harnessed for manipulation of cold atoms. The structural stability of catastrophes provides inherent robustness against variations in the system's dynamics and initial conditions, making them suitable for manipulation of atoms under imperfect conditions and limited controllability., Comment: 7 pages, 5 figures

We demonstrate, theoretically and experimentally, nonbroadening optical beams propagating along any arbitrarily chosen convex trajectory in space. We present a general method to construct such beams, and demonstrate it by generating beams following polynomial and exponential trajectories. We find that all such beams, accelerating along any convex trajectory, display the same universal intensity cross section, irrespective of their acceleration. The universal features of these beams are explored using catastrophe theory.

A linear self-referenced technique for temporal characterization of ultraweak pulse trains is presented. Shot-noise limited time-resolved single photon detection enables temporal resolution down to 10fs for pulse trains with ∼ 1 photon per pulse.

We study high-order harmonic generation in aligned molecules close to the ionization threshold. Two distinct contributions to the harmonic signal are observed, which show very different responses to molecular alignment and ellipticity of the driving field. We perform a classical electron trajectory analysis, taking into account the significant influence of the Coulomb potential on the strong-field-driven electron dynamics. The two contributions are related to primary ionization and excitation processes, offering a deeper understanding of the origin of high harmonics near the ionization threshold. This work shows that high harmonic spectroscopy can be extended to the near-threshold spectral range, which is in general spectroscopically rich., 4 pages, 4 figures

We present a new approach to probe the High-Harmonic Generation process. We use aligned molecules to study below-threshold harmonics and identify two distinct contributions to the emitted harmonics.

We demonstrate an optical nonlinearity free ultrashort pulse characterization technique relying on spectral component localization in time domain. Ultraweak pulses in NIR to XUV range can be characterized with resolution depending only on integration time.

We study the properties of an arbitrary microswimmer towing a passive load through a viscous liquid. The simple close-form expression for the dragging efficiency of a microswimmer dragging a distant load is found, and the approximation for finite mutual proximity is derived. We show that, while the swimmer can be arbitrarily efficient, the dragging efficiency is always bounded from above. It is also demonstrated, that opposite to Purcell's assumption [E. M. Purcell, Proc. Natl. Acad. Sci. U.S.A. 94, 11307 (1997)], the hydrodynamic coupling can "help" the propeller to tow the load. We support our conclusions by rigorous numerical calculations for the rotary swimmer, towing a spherical cargo positioned at a finite distance.

We present a simple, two dimensional example of a "cat" -- a body with zero angular momentum that can rotate itself with no external forces. This model is used to explain why this problem is known to be a gauge theory and to illustrate the importance of non-commutative operators. We will also show a comparison between the free-space "cat" in Newtonian mechanics and the same problem in Aristotelian mechanics at low Reynolds number; this simple example shows the analogy between (angular) momentum in Newtonian mechanics and (torque) force in Aristotelian mechanics. We will end by pointing out a topological invariant common to our model in free space and at low Reynolds number., Comment: 13 pages, 5 figures

We develop a qualitative geometric approach to swimming at low Reynolds number which avoids solving differential equations and uses instead landscape figures of two notions of curvatures: The swimming curvature and the curvature derived from dissipation. This approach gives complete information for swimmers that swim on a line without rotations and gives the main qualitative features for general swimmers that can also rotate. We illustrate this approach for a symmetric version of Purcell's swimmer which we solve by elementary analytical means within slender body theory. We then apply the theory to derive the basic qualitative properties of Purcell's swimmer., 24 pages, 12 figures

For large enough aspect ratio, we find better stroke patterns then the patterns proposed by D. Tam and A.P.Hosoi in their letter to PRL "Optimal Stroke Patterns for Purcell's Three-Link Swimmer"., Comment: 3 page, 1 figure

Phase measurement is a long-standing challenge in a wide range of applications, from X-ray imaging to astrophysics and spectroscopy. While in some scenarios the phase is resolved by an interferometric measurement, in others it is reconstructed via numerical optimization, based on some a-priori knowledge about the signal. The latter commonly use iterative algorithms, and thus have to deal with their convergence, stagnation, and robustness to noise. Here we combine these two approaches and present a new scheme, termed double blind Fourier holography, providing an efficient solution to the phase problem in two dimensions, by solving a system of linear equations. We present and experimentally demonstrate our approach for the case of lens-less imaging.

The application of catastrophe theory to high-harmonic generation is creating opportunities for optimizing the spectral intensity of extreme-ultraviolet light and characterizing attosecond pulses, explains Oren Raz from the Weizmann Institute of Science in Israel.

Ultrafast science is inherently, due to the lack of fast enough detectors and electronics, based on nonlinear interactions. Typically, however, nonlinear measurements require significant powers and often operate in a limited spectral range. Here we overcome the difficulties of ultraweak ultrafast measurements by precision time-domain localization of spectral components. We utilize this for linear self-referenced characterization of pulse trains having ∼ 1 photon per pulse, a regime in which nonlinear techniques are impractical, at a temporal resolution of ∼ 10 fs. This technique does not only set a new scale of sensitivity in ultrashort pulse characterization, but is also applicable in any spectral range from the near-infrared to the deep UV.

Simple, linear equations relate microscopic swimmers to the corresponding gliders and pumps. They have the following set of consequences: the swimming velocity of free swimmers can be inferred from the force on the tethered swimmer and vice versa; a tethered swimmer dissipates more energy than a free swimmer; it is possible to swim with arbitrarily high efficiency, but it is impossible to pump with arbitrarily high efficiency and finally that pumping is geometric. We also solve several optimization problems associated with swimming and pumping: the problem of optimal anchoring for a certain class of swimmers that includes the Purcell swimmer and the three linked spheres and the optimal geometries of helices considered as swimmers and pumps.

Many intriguing phenomena in nature—from phase transitions to black holes—occur at singularities. A unique type of singularity common in wave phenomena, known as caustics1,2, links processes observed in many different branches of physics3,4. Here, we investigate the role of caustics in attosecond science and in particular the physical process behind high harmonic generation5. We experimentally demonstrate spectral focusing in high harmonic generation, showing a robust intensity enhancement of an order of magnitude over a spectral width of several harmonics. This new level of control holds promises in both scientific and technological aspects of attosecond science6,7. Moreover, our study provides a deeper insight into the basic mechanism underlying the high harmonic generation process, revealing its quantum nature8 and universal properties. By applying catastrophe theory to high-harmonic generation, researchers identify caustics relating to regions of spectral focusing and greatly enhanced field intensity.