We present a theoretical study of ghost imaging by using blackbody radiation source. A Gaussian thin lens equation for the ghost imaging, which depends on both paths, is derived. The dependences of the visibility and quality of the image on the transverse size and temperature of the blackbody are studied. The main differences between the ghost imaging by using the blackbody radiation and by using the entangled photon pairs are image-forming equation, and the visibility and quality of the image
Within the Bose-Einstein statistics it is shown that the blackbody radiation contains coalescent photons along with single photons. Coalescent photons were first observed in the famous Hong-Ou-Mandel experiment of 1987. For the sake of convenience, $N$ coalescent photons are referred to as the $N$-photon cluster. In this work, statistics of photon clusters and probability that a photon cluster contains $N$ photons are found versus radiation frequency and temperature. Spectra of photon-cluster radiation are calculated as functions of blackbody temperature for different cluster ranks. Derivation…
Based on the general expressions for the tangential force and heating rate of a small polarizable particle during translational-rotational motion in the field of blackbody radiation (in the reference frame of latter),the tangential force in reference frame comoving with particle is calculated. It is this force determines the particle deceleration in the frame of reference of blackbody radiation.
A general expression is derived for the momentum diffusion constant of a small polarizable particle in blackbody radiation, and is shown to be closely related to the long-wavelength collisional decoherence rate for such a particle in a thermal environment. We show how this diffusion constant appears in the steady-state photon emission rate of two dipoles induced by blackbody radiation. We consider in addition the Einstein--Hopf drag force on a small polarizable particle moving in a blackbody field, and derive its fully relativistic form from the Lorentz transformation of forces.
The blackbody is considered in the external general field. The additional coefficients of stimulated emission and absorption are introduced into the Einstein mechanism. Then, the generalized Planck formula is derived. The Einstein and Debye formula for the specific heat is possible to generalize. The application of the theory to the sonoluminescence, the relic radiation and solar spectrum is discussed.
We consider the general open system problem of a charged quantum oscillator confined in a harmonic trap, whose frequency can be arbitrarily modulated in time, that interacts with both an incoherent quantized (blackbody) radiation field and with an arbitrary coherent laser field. We assume that the oscillator is initially in thermodynamic equilibrium with its environment, a non-factorized initial density matrix of the system and the environment, and that at $t=0$ the modulation of the frequency, the coupling to the incoherent and the coherent radiation are switched on. The subsequent dynamics, …
Motivated by the prospect of an optical frequency standard based on 43Ca+, we calculate the blackbody radiation (BBR) shift of the 4s_1/2-3d_5/2 clock transition, which is a major component of the uncertainty budget. The calculations are based on the relativistic all-order single-double method where all single and double excitations of the Dirac-Fock wave function are included to all orders of perturbation theory. Additional calculations are conducted for the dominant contributions in order to evaluate some omitted high-order corrections and estimate the uncertainties of the final results. The…
The problem of blackbody radiation in flat space with non-compact extra dimensions was analysed recently. In the present article we reanalyse this problem with compact (and non-compact) extra dimensions in flat space to observe the consequences of this approach upon Wien's displacement and Stefan-Boltzmann law.
We present a simple calculation of the Lorentz transformation of the spectral distribution of blackbody radiation at temperature T. Here we emphasize that T is the temperature in the blackbody rest frame and does not change. We thus avoid the confused and confusing question of how temperature transforms. We show by explicit calculation that at zero temperature the spectral distribution is invariant. At finite temperature we find the well known result familiar in discussions of the the 2.7! K cosmic radiation.
Blackbody radiation around hot objects induces ac Stark shifts of the energy levels of nearby atoms and molecules. These shifts are roughly proportional to the fourth power of the temperature and induce a force decaying with the third power of the distance from the object. We explicitly calculate the resulting attractive blackbody optical dipole force for ground state hydrogen atoms. Surprisingly, this force can surpass the repulsive radiation pressure and actually pull the atoms against the radiation energy flow towards the surface with a force stronger than gravity. We exemplify the dominanc…
The blackbody radiation is analyzed in universes with $D$ spatial dimensions. With the classical electrodynamics suited to the universe in focus and recurring to the hyperspherical coordinates, it is shown that the spectral energy density as well as the total energy density are sensible to the dimensionality of the universe. Wien's displacement law and the Stefan-Boltzmann law are properly generalized.
We introduce a biparametric Fisher-Rényi complexity measure for general probability distributions and we discuss its properties. This notion, which is composed of two entropy-like components (the Rényi entropy and the biparametric Fisher information), generalizes the basic Fisher-Shannon measure and the previous complexity quantifiers of Fisher-Rényi type. Then, we illustrate the usefulness of this notion by carrying out a information-theoretical analysis of the spectral energy density of a $d$-dimensional blackbody at temperature $T$. It is shown that the biparametric Fisher-Rényi measure of …
Light from thermal black body radiators such as stars exhibits photon bunching behaviour at sufficiently short timescales. However, with available detector bandwidths, this bunching signal is difficult to be directly used for intensity interferometry with sufficient statistics in astronomy. Here we present an experimental technique to increase the photon bunching signal in blackbody radiation via spectral filtering of the light source. Our measurements reveal strong temporal photon bunching in light from blackbody radiation, including the Sun. Such filtering techniques may revive the interest …
Precision measurements of quantum systems often seek to probe or must account for the interaction with blackbody radiation. Over the past several decades, much attention has been given to AC Stark shifts and stimulated state transfer. For a blackbody in thermodynamic equilibrium, these two effects are determined by the expectation value of photon number in each mode of the Planck spectrum. Here, we explore how the photon number variance of an equilibrium blackbody generally leads to a parametric broadening of the energy levels of quantum systems that is inversely proportional to the square-roo…
We report experimental measurements of the rates of blackbody radiation-induced transitions between high-lying (n>60) S, P and D Rydberg levels of rubidium atoms in a magneto-optical trap using a hybrid field ionization and state-selective depumping technique. Our results reveal significant deviations of the measured transition rates from theory for well-defined ranges of the principal quantum number. We assume that the most likely cause for those deviations is a modified blackbody spectrum inside the glass cell in which the magneto-optical trap is formed, and we test this assumption by instal…
More general canonical ensemble which gives rise the generalized statistics or $q$-deformed statistics can represent the realistic scenario than the ideal one, with proper parameter sets involved. We study the Planck's law of blackbody radiation, Wein's and Rayleigh-Jeans radiation formulae from the point of view of $q$-deformed statistics. We find that the blackbody energy spectrum curve for a given temperature $T$ corresponding to different $q$ values differs from each other: the location of the peak(i.e. $ν_m$) of the energy distribution $u_ν$ (corresponding to different $q$ ) shifted towar…
The operation of atomic clocks is generally carried out at room temperature, whereas the definition of the second refers to the clock transition in an atom at absolute zero. This implies that the clock transition frequency should be corrected in practice for the effect of finite temperature of which the leading contributor is the blackbody radiation (BBR) shift. Experimental measurements of the BBR shifts are difficult. In this work, we have calculated the blackbody radiation shift of the ground-state hyperfine microwave transition in 87Rb using the relativistic all-order method and carried ou…
We measure the dynamic differential scalar polarizabilities at 10.6 $μ$m for two candidate clock transitions in $^{176}\mathrm{Lu}^+$. The fractional black body radiation (BBR) shifts at 300 K for the $^1S_0 \leftrightarrow {^3D_1}$ and $^1S_0 \leftrightarrow {^3D_2}$ transitions are evaluated to be $-1.36\,(9) \times 10^{-18}$ and $2.70 \,(21) \times10^{-17}$, respectively. The former is the lowest of any established optical atomic clock.
We investigate the radiation of a blackbody in a cavity of finite size. For a given geometry, we use semiclassical techniques to obtain explicit expressions of the modified Planck's and Stefan-Boltzmann's blackbody radiation laws as a function of the size and shape of the cavity. We determine the range of parameters (temperature, size and shape of the cavity) for which these effects are accessible to experimental verification. Finally we discuss potential applications of our findings in the physics of the cosmic microwave background and sonoluminescence.
A non-local gauge symmetry of a complex scalar field, which can be trivially extended to spinor fields, was demonstrated in a recent paper (Mod.Phys.Lett. A13, 1265 (1998) ; hep-th/9902020). The corresponding covariant Lagrangian density yielded a new, non-local Quantum Electrodynamics. In this letter we show that as a consequence of this new QED, a blackbody radiation viewed through gaseous matter appears to show a slight deviation from the Planck formula, and propose an experimental test to check this effect. We also show that a non-uniformity in this gaseous matter distribution leads to an …
Nanomechanical systems are generally embedded in a macroscopic environment where the sources of thermal noise are difficult to pinpoint. We engineer a silicon nitride membrane optomechanical resonator such that its thermal noise is acoustically driven by a spatially well-defined remote macroscopic bath. This bath acts as an acoustic blackbody emitting and absorbing acoustic radiation through the silicon substrate. Our optomechanical system acts as a sensitive detector for the blackbody temperature and for photoacoustic imaging. We demonstrate that the nanomechanical mode temperature is governe…
The translational motion of molecular ions can be effectively cooled sympathetically to temperatures below 100 mK in ion traps through Coulomb interactions with laser-cooled atomic ions. The distribution of internal rovibrational states, however, gets in thermal equilibrium with the typically much higher temperature of the environment within tens of seconds. We consider a concept for rotational cooling of such internally hot, but translationally cold heteronuclear diatomic molecular ions. The scheme relies on a combination of optical pumping from a few specific rotational levels into a ``dark …
We have determined the frequency shift that blackbody radiation is inducing on the $5s^2$ $^1$S$_0$ -- $5s5p$ $^3$P$_0$ clock transition in strontium. Previously its uncertainty limited the uncertainty of strontium lattice clocks to $1\times10^{-16}$. Now the uncertainty associated to the black body radiation shift correction translates to $5\times 10^{-18}$ relative frequency uncertainty at room temperature. Our evaluation is based on a measurement of the differential dc-polarizability of the two clock states and on a modeling of the dynamic contribution using this value and experimental data…
In a recent work, we have derived simple Lindblad-based equations for the thermalization of systems in contact with a thermal reservoir. Here, we apply these equations to the Lipkin-Meshkov-Glick model (LMG) in contact with a blackbody radiation and analyze the dipole matrix elements involved in the thermalization process. We find that the thermalization can be complete only if the density is sufficiently high, while, in the limit of low density, the system thermalizes partially, namely, within the Hilbert subspaces where the total spin has a fixed value. In this regime, and in the isotropic c…
The use of x-ray imaging in medicine and other research is well known. Generally, the image quality is proportional to the total flux, but high photon energy could severely damage the specimen, so how to decrease the radiation dose while maintaining image quality is a fundamental problem. In "ghost" imaging, an image is retrieved from a known patterned illumination field and the total intensity transmitted through the object collected by a bucket detector. Using a table-top x-ray source we have realized ghost imaging of plane and natural objects with ultra-low radiation on the order of single …
In this work we generalize the Stefan-Boltzmann and Wien's displacement laws for a $D$-dimensional manifold composed by 4 non-compact dimensions and $D-4$ compact dimensions, $ R^{1,3}$ x $T^{D-4} $. The electromagnetic field is assumed to pervade all compact and non-compact dimensions. In particular, the total radiated power becomes $ R(T) = σ_B T^4 + σ_D (a) \, T^D $, where $a$ is the size of the compact extra dimensions. For $D=10$, predicted from String Theory, and $D=11$, from M-Theory, the outcomes agree with available experimental data for $a$ as high as 2 x $10^{-7}$m.
The X-ray free electron lasers (XFEL) can enable diffractive structural determination of protein crystals or single molecules that are too radiation-sensitive for conventional X-ray analysis. However the electronic form factor could have been modified during the ultrashort X-ray pulse due to photoionization and electron cascade caused by the intense X-ray pulse. For general X-ray imaging techniques, to minimize radiation damage effect is of major concern to ensure faithful reconstruction of the structure. Here we show that a radiation-damage-free diffraction can be achieved with an atomic spat…
An ensemble of excited atoms can synchronize emission of light collectively in a process known as superradiance when its characteristic size is smaller than the wavelength of emitted photons. The underlying superradiance depends strongly on electromagnetic (photon) fields surrounding the atomic ensemble. High mode densities of microwave photons from $300\,$K blackbody radiation (BBR) significantly enhance decay rates of Rydberg states to neighbouring states, enabling superradiance that is not possible with bare vacuum induced spontaneous decay. Here we report observations of the superradiance …
We develop a nonstandard concept of atomic clocks where the blackbody radiation shift (BBRS) and its temperature fluctuations can be dramatically suppressed (by one to three orders of magnitude) independent of the environmental temperature. The suppression is based on the fact that in a system with two accessible clock transitions (with frequencies v1 and v2) which are exposed to the same thermal environment, there exists a "synthetic" frequency v_{syn} (v1-e12 v2) largely immune to the BBRS. As an example, it is shown that in the case of ion 171Yb+ it is possible to create a clock in which th…
We show that three group IIIB divalent ions, B+, Al+, and In+, have anomalously small blackbody radiation (BBR) shifts of the ns^2 1S0 - nsnp 3P0 clock transitions. The fractional BBR shifts for these ions are at least 10 times smaller than those of any other present or proposed optical frequency standards at the same temperature, and are less than 0.3% of the Sr clock shift. We have developed a hybrid configuration interaction + coupled-cluster method that provides accurate treatment of correlation corrections in such ions, considers all relevant states in the same systematic way, and yields …
We evaluated the C_6 coefficients of Yb-Yb and Yb -alkali/group II van der Waals interactions with 2% uncertainty. The only existing results for such quantities are for the Yb-Yb dimer. Our value, C_6=1929(39) a.u., is in excellent agreement with the recent experimental determination of 1932(35) a.u. We have also developed a new approach for the calculation of the dynamic correction to the blackbody radiation shift. We have calculated this quantity for the Yb 6s^2 ^1S_0 - 6s6p ^3P_0 clock transition with 3.5% uncertainty. This reduces the fractional uncertainty due to the blackbody radiation s…
Results of theoretical calculations of ionization rates of Rb and Na Rydberg atoms by blackbody radiation (BBR) are presented. Calculations have been performed for nS, nP and nD states of Na and Rb, which are commonly used in a variety of experiments, at principal quantum numbers n=8-65 and at three ambient temperatures of 77, 300 and 600 K. A peculiarity of our calculations is that we take into account the contributions of BBR-induced redistribution of population between Rydberg states prior to photoionization and field ionization by extraction electric field pulses. The obtained results show…
We study the thermalization of an ensemble of $N$ elementary, arbitrarily-complex, quantum systems, mutually noninteracting but coupled as electric or magnetic dipoles to a blackbody radiation. The elementary systems can be all the same or belong to different species, distinguishable or indistinguishable, located at fixed positions or having translational degrees of freedom. Even if the energy spectra of the constituent systems are nondegenerate, as we suppose, the ensemble unavoidably presents degeneracies of the energy levels and/or of the energy gaps. We show that, due to these degeneracies…
We evaluated the static and dynamic polarizabilities of the 5s^2 ^1S_0 and 5s5p ^3P_0^o states of Sr using the high-precision relativistic configuration interaction + all-order method. Our calculation explains the discrepancy between the recent experimental 5s^2 ^1S_0 - 5s5p ^3P_0^o dc Stark shift measurement Δα= 247.374(7) a.u. [Middelmann et. al, arXiv:1208.2848 (2012)] and the earlier theoretical result of 261(4) a.u. [Porsev and Derevianko, Phys. Rev. A 74, 020502R (2006)]. Our present value of 247.5 a.u. is in excellent agreement with the experimental result. We also evaluated the dynamic…
The operation of atomic clocks is generally carried out at room temperature, whereas the definition of the second refers to the clock transition in an atom at absolute zero. This implies that the clock transition frequency should be corrected in practice for the effect of finite temperature of which the leading contributor is the blackbody radiation (BBR) shift. In the present work, we used configuration interaction + coupled-cluster method to evaluate polarizabilities of the $6s^2 ^1S_0$ and $6s6p ^3P_0$ states of Tl$^+$ ion; we find $α_0(^1S_0)=19.6$ a.u. and $α_0(^3P_0)=21.4$ a.u.. The resu…
A systematic study of Ca+ atomic properties is carried out using high-precision relativistic all-order method where all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. Reduced matrix elements, oscillator strengths, transition rates, and lifetimes are determined for the levels up to n = 7. Recommended values and estimates of their uncertainties are provided for a large number of electric-dipole transitions. Electric-dipole scalar polarizabilities for the 5s, 6s, 7s, 8s, 4p, 5p, 3d, and 4d states and tensor polari…
In this work we obtain Planck's blackbody spectrum from the thermal scalar radiation contained in a resonant cavity of volume V in the context of classical mechanics, which provides the classical zero-point electromagnetic radiation in terms of a scale parameter that depends on geometric properties of the enclosure and electrical magnitudes. The scale parameter of the classical zero-point electromagnetic radiation is associated to experimental measurements of Casimir forces, but we show that theoretically its value for known radiant cavities that approach a blackbody has a numerical value of t…
A major obstacle for optical clocks is the frequency shift due to black body radiation. We discuss how one can tackle this problem in an optical lattice clock; in our case 87-Sr: firstly, by a measurement of the dc Stark shift of the clock transition and, secondly, by interrogating the atoms in a cryogenic environment. Both approaches rely on transporting ultracold atoms over several cm within a probe cycle. We evaluate this approach of mechanically moving the optical lattice and conclude that it is feasible to transport the atoms over 50 mm within 300 ms. With this transport a dc Stark shift …
Rydberg atoms excited by cold blackbody radiation are shown to display long-lived quantum coherences on timescales of tens of picoseconds. By solving non-Markovian equations of motion with no free parameters we obtain the time evolution of the density matrix, and demonstrate that the blackbody-induced temporal coherences manifest as slowly decaying (100 ps) quantum beats in time-resolved fluorescence. An analytic model shows the dependence of the coherent dynamics on the energy splitting between atomic eigenstates, transition dipole moments, and coherence time of the radiation. Experimental de…
We reconsider the black hole firewall puzzle, emphasizing that quantum error-correction, computational complexity, and pseudorandomness are crucial concepts for understanding the black hole interior. We assume that the Hawking radiation emitted by an old black hole is pseudorandom, meaning that it cannot be distinguished from a perfectly thermal state by any efficient quantum computation acting on the radiation alone. We then infer the existence of a subspace of the radiation system which we interpret as an encoding of the black hole interior. This encoded interior is entangled with the late o…
Nearly all thermal radiation phenomena involving materials with linear response can be accurately described via semi-classical theories of light. Here, we go beyond these traditional paradigms to study a nonlinear system which, as we show, necessarily requires quantum theory of damping. Specifically, we analyze thermal radiation from a resonant system containing a $χ^{(2)}$ nonlinear medium and supporting resonances at frequencies $ω_1$ and $ω_2\approx 2ω_1$, where both resonators are driven only by intrinsic thermal fluctuations. Within our quantum formalism, we reveal new possibilities for s…
Despite being a canonical example of quantum mechanical perturbation theory, as well as one of the earliest observed spectroscopic shifts, the Stark effect contributes the largest source of uncertainty in a modern optical atomic clock through blackbody radiation. By employing an ultracold, trapped atomic ensemble and high stability optical clock, we characterize the quadratic Stark effect with unprecedented precision. We report the ytterbium optical clock's sensitivity to electric fields (such as blackbody radiation) as the differential static polarizability of the ground and excited clock lev…
