Number Of Pure States Research Articles

Jordan in The Church of The Higher Hilbert Space: Entanglement and Thermal Fluctuations

I revisit Jordan's derivation of Einstein's formula for energy fluctuations in the black body in thermal equilibrium. This formula is usually taken to represent the unification of the wave and the particle aspects of the electromagnetic field since the fluctuations can be shown to be the sum of wave-like and particle-like contributions. However, in Jordan's treatment there is no mention of the Planck distribution and all averages are performed with respect to pure number states of radiation (mixed states had not yet been discovered!). The chief reason why Jordan does reproduce Einstein's result despite not using thermal states of radiation is that he focuses on fluctuations in a small (compared to the whole) volume of the black body. The state of radiation in a small volume is highly entangled to the rest of the black body which leads to the correct fluctuations even though the overall state might, in fact, be assumed to be pure (i.e. at zero temperature). I present a simple derivation of the fluctuations formula as an instance of mixed states being reductions of higher level pure states, a representation that is affectionately known as "Church of the Higher Hilbert Space". According to this view of mixed states, temperature is nothing but the amount of entanglement between the system and its environment.Quanta 2022; 11: 1–4.

Chaotic temperature and bond dependence of four-dimensional Gaussian spin glasses with partial thermal boundary conditions

Spin glasses have competing interactions and complex energy landscapes that are highly-susceptible to perturbations, such as the temperature or the bonds. The thermal boundary condition technique is an effective and visual approach for characterizing chaos, and has been successfully applied to three dimensions. In this paper, we tailor the technique to partial thermal boundary conditions, where thermal boundary condition is applied in a subset (3 out of 4 in this work) of the dimensions for better flexibility and efficiency for a broad range of disordered systems. We use this method to study both temperature chaos and bond chaos of the four-dimensional Edwards-Anderson model with Gaussian disorder to low temperatures. We compare the two forms of chaos, with chaos of three dimensions, and also the four-dimensional $\pm J$ model. We observe that the two forms of chaos are characterized by the same set of scaling exponents, bond chaos is much stronger than temperature chaos, and the exponents are also compatible with the $\pm J$ model. Finally, we discuss the effects of chaos on the number of pure states in the thermal boundary condition ensemble.

Simultaneous polarization squeezing in polarized N photon state and diminution on a squeezing operation

We study polarization squeezing of a pure photon number state, which is obviously polarized but the mere change in the basis of polarization leads to simultaneous polarization squeezing in all the components of Stokes operator vector except those falling along or perpendicular to the direction of polarization state, is observed. We use the most general definition of polarization squeezing and discuss the experimental feasibility of the result. We also observe that a squeezing operation like non-degenerate parametric amplification of the state does not reveal simultaneous squeezing in all Stokes operator vectors and decreases in this sense.

Photon Counting for a Number State Passing through a Laser Channel

We investigate the photon counting for a pure number state passing through a laser channel. It is found that the pure number state evolves in the laser channel into a mixed state: the number state |m〉〈m| evolves into a superposition of the photon-added thermal (chaotic) state, and the photon counting for the outcome state is a Gauss hypergeometric function.

A New Binomial–Negative-Binomial Combinatorial State in Quantum Optics Theory and Its Generation

Based on the concept of the binomial state and the negative-binomial state we introduce a new binomial–negative-binomial combinatorial state in quantum optics theory. We show that such a state can be implemented in the laser channel as an output state when the initial state is a pure number state. The master equation related to the laser channel is solved by virtue of the entangled state representation.

S-Parameterized photocount formula

AbstractEmploying the s-ordered operator expansion formula and the technique of integration within s-ordered product of operators, we derive a new photocount formula for general parameter s, which can unify the two quantum-mechanical photocount formulas in Opt. Lett. 33, 433 (2008). It brings convenience to photocount’s calculation when system’s density operator is known. The s-parameterized photocount formula for pure number state density operator is firstly derived.

Solving nonlinear master equation describing quantum damping by virtue of the entangled state representation

This paper solves the newly constructed nonlinear master equation dρ/dt = κ[2f (N) aρ (1/f (N − 1))a† − a†aρ−ρa†a], where f(N) is an operator-valued function of N = a†a, for describing amplitude damping channel, and derives the infinite operator sum representation of quasi-Kraus operators for the density operator. It also shows that in this nonlinear process the initial pure number state density operator will evolve into the binomial field (a mixed state) when

Evolution of Number State to Density Operator of Binomial Distribution in the Amplitude Dissipative Channel

We show that passing through the amplitude dissipative channel the initial pure number state density operator is evolved into the density operator of binomial distribution (a mixed state), and the binomial distribution parameter is just equal to e−2kt, where k is the dissipative parameter of the channel. We solve the corresponding master equation to obtain the operator-sum representation of the density operator by virtue of the entangled state representation, which seems to be a convenient approach.

Bridging visible and telecom wavelengths with a single-mode broadband photon pair source

We present a spectrally decorrelated photon pair source bridging the visible and telecom wavelength regions. Tailored design and fabrication of a solid-core photonic crystal fiber (PCF) lead to the emission of signal and idler photons into only a single spectral and spatial mode. Thus no narrowband filtering is necessary and the heralded generation of pure photon number states in ultrafast wave packets at telecom wavelengths becomes possible.

Intrinsic phase coherence of laser light

We examine the phase relationships between different packets of a beam of light emitted from a cavity through a partially transmitting mirror. We find that the beam has a pronounced phase coherence even when the intracavity field has a completely indeterminate phase such as, for example, when it is in a pure photon number state. In this case, the phase coherence can be directly attributed to entanglement caused by the partially transmitting mirror and, even though the external light has phase coherence, it has no identifiable phase. Consequently there is no phase diffusion but there is diffusion of the phase difference between a packet and the intracavity field. Remarkably, we find that the phase coherence of the beam is almost independent of the intracavity state, provided this has a reasonably narrow number-state distribution about a large mean value.

Bounds on Multipartite Entangled Orthogonal State Discrimination Using Local Operations and Classical Communication

We show that entanglement guarantees difficulty in the discrimination of orthogonal multipartite states locally. The number of pure states that can be discriminated by local operations and classical communication is bounded by the total dimension over the average entanglement. A similar, general condition is also shown for pure and mixed states. These results offer a rare operational interpretation for three abstractly defined distancelike measures of multipartite entanglement.

Emission and cavity-field spectra in a cascade three-level system interacting with a single-mode field

By using the method of eigenvalues and eigenstates, the emission and cavity-field spectra of a cascade three-level atom interacting with a single-mode electromagnetic field are studied in both intensity-dependent coupling (IDC) and intensity-independent coupling (IIC) cases. The photon statistics of the field on the spectra are investigated for the initial field in the pure number state, the coherent state and the thermal state. In the resonant case and the strong field limit, the pure-number-state emission spectrum exhibits six peaks and three peaks, respectively, for the IDC case and the IIC case. For a strong initial coherent state field or a strong thermal state field, the central structure of the emission spectrum at the field frequency is a doublet in the IDC case and a singlet in the IIC case. The cavity-field spectrum has three peaks in the IDC case and a single peak in the IIC case in the strong field limit for all of the three kinds of initial fields considered. Results indicate that in the emission spectrum merging of spectral peaks occurs for the IIC case as the initial field becomes stronger while it does not happen for the IDC case.

Influence of AC-Stark shift on cavity field spectra in the non-degenerate Raman process

The cavity field spectrum of an atom interacting with two-mode field through non-degenerate Raman coupling with the presence of AC-Stark shift in an ideal cavity is investigated. The results for the atom in the low-level state and the initial fields in pure number states, coherent states, and squeezed vacuum states are calculated. When the initial fields are in number states, the three-peak structure of each model cavity field spectra appear for weak fields, and two-peak or single-peak structure appear for strong fields. When both field modes are in a superposition of number states initially, the cavity field spectra are generally of two-peak structure. With the increase of γ=g2/g1,one peak rises and the other peak reduces.

Cavity Field Spectra of the Intensity-Dependent Two-Mode Jaynes–Cummings Model

The cavity field spectrum of a two-level atom interacting with two modes of the radiation field through intensity-dependent coupling in an ideal cavity is investigated. The results for the initial fields in pure number states, coherent states, and squeezed vacuum states are calculated. We find that the frequency of one mode is tuned by the intensity of the other mode when the two modes are both in pure number states or coherent states. A complicated multipeak structure appears when both field modes are in a superposition of number states initially.

Numerical Evidence of Infinite Number of Pure States Near Ferromagnetic Phase Boundary for Short-Range Spin-Glass Systems

Numerical evidence that the number of pure states in the spin glass phase is infinite near the ferromagnetic phase boundary for the three dimensional (3D) ± J Ising model and 3D gauge glass models ...

Emission spectrum of a Λ-type three-level atom driven by the squeezed coherent field and grey-body radiation field

By means of quantum electrodynamics, an analytical expression of emission spectrum for a Λ-type three-level atom with the two non-degenerate lower levels in the cavity is given. The character of the emission spectrum for the input in pure number state, a squeezed coherent state and grey-body state are exhibited. The effects of the atomic initial state, the field property, the cavity absorptivity and the system temperature on the time-dependent physical spectrum are analysed.

CAVITY FIELD SPECTRA OF AN ATOM INTERACTING WITH TWO-MODE FIELD THROUGH RAMAN PROCESS

The cavity field spectra of a two level atom interacting with two mode field through Raman process are investigated. It is shown that the basic features of the spectra is unchanged whether the atom is in the high or low level state initially. Symmetrical two peak structure appears in the spectrum for each mode when the initial fields are both in the pure number states or both in the coherent states. The split of the two peaks is proportional to the field intensity of the other mode.

Preparing pure photon number states of the radiation field

The quantum mechanical description of a radiation field is based on states that are characterized by the number of photons in a particular mode; the most basic quantum states are those with fixed photon number, usually referred to as number (or Fock) states. Although Fock states of vibrational motion can be observed readily in ion traps, number states of the radiation field are very fragile and difficult to produce and maintain. Single photons in multi-mode fields have been generated using the technique of photon pairs. But in order to generate these states in a cavity, the mode in question must have minimal losses; moreover, additional sources of photon number fluctuations, such as the thermal field, must be eliminated. Here we observe the build-up of number states in a high-Q cavity, by investigating the interaction dynamics of a probe atom with the field. We employ a dynamical method of number state preparation that involves state reduction of highly excited atoms in a cavity, with a photon lifetime as high as 0.2 seconds. (This set-up is usually known as the one-atom maser or 'micromaser'.) Pure states containing up to two photons are measured unambiguously.

CAVITY FIELD SPECTRA OF THE TWO-ATOM TWO-PHOTON JAYNES-CUMMINGS MODEL

The cavity field spectra for a pair of coupled two-level atoms with single mode of the radiation in an ideal cavity via two-photon resonant transition processes are investigated.The results for the initial fields in pure number state,coherent state or squ

Nondestructive optical measurement of relative phase between two Bose-Einstein condensates

We study the interaction of light with two Bose condensates as an open quantum system. The two overlapping condensates occupy two different Zeeman sublevels and two driving light beams induce a coherent quantum tunneling between the condensates. We derive the master equation for the system. It is shown that stochastic simulations of the measurements of spontaneously scattered photons establish the relative phase between two Bose condensates, even though the condensates are initially in pure number states. These measurements are non-destructive for the condensates, because only light is scattered, but no atoms are removed from the system. Due to the macroscopic quantum interference the detection rate of photons depends substantially on the relative phase between the condensates. This may provide a way to distinguish, whether the condensates are initially in number states or in coherent states.