Phase diagram of the spin-1/2 triangular J1-J2 Heisenberg model on a three-leg cylinder

We study the phase diagram of the frustrated Heisenberg model on the triangular lattice with nearest- and next-nearest-neighbor spin-exchange coupling, on three-leg ladders. Using the density-matrix renormalization-group method, we obtain the complete phase diagram of the model, which includes quasi-long-range 120° and columnar order, and a Majumdar-Ghosh phase with short-ranged correlations. All these phases are nonchiral and planar. We also identify the nature of phase transitions

Soliton-potential interaction in the nonlinear Klein-Gordon model

The interaction of solitons with external potentials in nonlinear Klein-Gordon field theory is investigated using an improved model. The presented model has been constructed with a better approximation for adding the potential to the Lagrangian through the metric of background space-time. The results of the model are compared with another model and the differences are discussed.Comment: 14 pages,8 figure

No Tradeoff between Coherence and Sub-Poissonianity for Heisenberg-Limited Lasers

The Heisenberg limit to laser coherence $\mathfrak{C}$ -- the number of photons in the maximally populated mode of the laser beam -- is the fourth power of the number of excitations inside the laser. We generalize the previous proof of this upper bound scaling by dropping the requirement that the beam photon statistics be Poissonian (i.e., Mandel's $Q=0$). We then show that the relation between $\mathfrak{C}$ and sub-Poissonianity ($Q<0$) is win-win, not a tradeoff. For both regular (non-Markovian) pumping with semi-unitary gain (which allows $Q\xrightarrow{}-1$), and random (Markovian) pumping with optimized gain, $\mathfrak{C}$ is maximized when $Q$ is minimized.Comment: This is a companion letter to the manuscript entitled "Optimized Laser Models with Heisenberg-Limited Coherence and Sub-Poissonian Beam Photon Statistics", arxiv:2208.14082. 6 pages, 2 figure

The Heisenberg limit for laser coherence

To quantify quantum optical coherence requires both the particle- and wave-natures of light. For an ideal laser beam [1,2,3], it can be thought of roughly as the number of photons emitted consecutively into the beam with the same phase. This number, $\mathfrak{C}$, can be much larger than $\mu$, the number of photons in the laser itself. The limit on $\mathfrak{C}$ for an ideal laser was thought to be of order $\mu^2$ [4,5]. Here, assuming nothing about the laser operation, only that it produces a beam with certain properties close to those of an ideal laser beam, and that it does not have external sources of coherence, we derive an upper bound: $\mathfrak{C} = O(\mu^4)$. Moreover, using the matrix product states (MPSs) method [6,7,8,9], we find a model that achieves this scaling, and show that it could in principle be realised using circuit quantum electrodynamics (QED) [10]. Thus $\mathfrak{C} = O(\mu^2)$ is only a standard quantum limit (SQL); the ultimate quantum limit, or Heisenberg limit, is quadratically better.Comment: 6 pages, 4 figures, and 31 pages of supplemental information. v2: This paper is now published [Nature Physics DOI:10.1038/s41567-020-01049-3 (26 October 2020)]. For copyright reasons, this arxiv paper is based on a version of the paper prior to the accepted (21 August 2020) versio

Optimized Laser Models with Heisenberg-Limited Coherence and Sub-Poissonian Beam Photon Statistics

Recently it has been shown that it is possible for a laser to produce a stationary beam with a coherence (quantified as the mean photon number at spectral peak) which scales as the fourth power of the mean number of excitations stored within the laser, this being quadratically larger than the standard or Schawlow-Townes limit [1]. Moreover, this was analytically proven to be the ultimate quantum limit (Heisenberg limit) scaling under defining conditions for CW lasers, plus a strong assumption about the properties of the output beam. In Ref. [2], we show that the latter can be replaced by a weaker assumption, which allows for highly sub-Poissonian output beams, without changing the upper bound scaling or its achievability. In this Paper, we provide details of the calculations in Ref. [2], and introduce three new families of laser models which may be considered as generalizations of those presented in that work. Each of these families of laser models is parameterized by a real number, $p$, with $p=4$ corresponding to the original models. The parameter space of these laser families is numerically investigated in detail, where we explore the influence of these parameters on both the coherence and photon statistics of the laser beams. Two distinct regimes for the coherence may be identified based on the choice of $p$, where for $p>3$, each family of models exhibits Heisenberg-limited beam coherence, while for $p<3$, the Heisenberg limit is no longer attained. Moreover, in the former regime, we derive formulae for the beam coherence of each of these three laser families which agree with the numerics. We find that the optimal parameter is in fact $p\approx4.15$, not $p=4$.Comment: This is a companion manuscript to the letter entitled "No Tradeoff between Coherence and Sub-Poissonianity for Heisenberg-Limited Lasers", arxiv:2208.14081. 22 pages, 11 figure

Gathering Anonymous, Oblivious Robots on a Grid

We consider a swarm of $n$ autonomous mobile robots, distributed on a 2-dimensional grid. A basic task for such a swarm is the gathering process: All robots have to gather at one (not predefined) place. A common local model for extremely simple robots is the following: The robots do not have a common compass, only have a constant viewing radius, are autonomous and indistinguishable, can move at most a constant distance in each step, cannot communicate, are oblivious and do not have flags or states. The only gathering algorithm under this robot model, with known runtime bounds, needs $\mathcal{O}(n^2)$ rounds and works in the Euclidean plane. The underlying time model for the algorithm is the fully synchronous $\mathcal{FSYNC}$ model. On the other side, in the case of the 2-dimensional grid, the only known gathering algorithms for the same time and a similar local model additionally require a constant memory, states and "flags" to communicate these states to neighbors in viewing range. They gather in time $\mathcal{O}(n)$. In this paper we contribute the (to the best of our knowledge) first gathering algorithm on the grid that works under the same simple local model as the above mentioned Euclidean plane strategy, i.e., without memory (oblivious), "flags" and states. We prove its correctness and an $\mathcal{O}(n^2)$ time bound in the fully synchronous $\mathcal{FSYNC}$ time model. This time bound matches the time bound of the best known algorithm for the Euclidean plane mentioned above. We say gathering is done if all robots are located within a $2\times 2$ square, because in $\mathcal{FSYNC}$ such configurations cannot be solved