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Girish Kulkarni

Publications and source records attributed to Girish Kulkarni.

At least 73 records · Page 4Linked to original sources
arXiv2022

A classical model of spontaneous parametric down-conversion

We model spontaneous parametric down-conversion (SPDC) as classical difference frequency generation (DFG) of the pump field and a hypothetical stochastic "vacuum" seed field. We analytically show that the second-order spatiotemporal correlations of the field generated from the DFG process replicate those of the signal field from SPDC. Specifically, for low gain, the model is consistent with the quantum calculation of the signal photon's reduced density matrix; and for high gain, the model's predictions are in good agreement with our experimental measurements of the far-field intensity profile, orbital angular momentum spectrum, and wavelength spectrum of the SPDC field for increasing pump strengths. We further theoretically show that the model successfully captures second-order SU(1,1) interference and induced coherence effects in both gain regimes. Intriguingly, the model also correctly predicts the linear scaling of the interference visibility with object transmittance in the low-gain regime -- a feature that is often regarded as a quintessential signature of the nonclassicality of induced coherence. Our model may not only lead to novel fundamental insights into the classical-quantum divide in the context of SPDC and induced coherence, but can also be a useful theoretical tool for numerous experiments and applications based on SPDC.

physics.optics↗
arXiv2022

The effect of inhomogeneous reionisation on the Lyman-$α$ forest power spectrum at redshift $z>4$: implications for thermal parameter recovery

We use the Sherwood-Relics suite of hybrid hydrodynamical and radiative transfer simulations to model the effect of inhomogeneous reionisation on the 1D power spectrum of the \Lya forest transmitted flux at redshifts $4.2\leq z \leq 5$. Relative to models that assume a homogeneous UV background, reionisation suppresses the power spectrum at small scales, $k \sim 0.1\rm\,km^{-1}\,s$ by $\sim 10$ per cent because of spatial variations in the thermal broadening kernel and the divergent peculiar velocity field associated with over-pressurised intergalactic gas. On larger scales, $k<0.03\rm\,km^{-1}\,s$, the power spectrum is instead enhanced by $10$--$50$ per cent by large scale spatial variations in the neutral hydrogen fraction. The effect of inhomogeneous reionisation must therefore be accounted for in analyses of forthcoming high precision measurements. We provide a correction for the Ly$α$ forest power spectrum at $4.1\leq z \leq 5.4$ that can be easily applied within other parameter inference frameworks using similar reionisation models. We perform a Bayesian analysis of mock data to assess the extent of systematic biases that may arise in measurements of the intergalactic medium if ignoring this correction. At the scales probed by current high resolution Ly$α$ forest data at $z>4$, $0.006 \rm \,km^{-1}\,s\leq k \leq 0.2 \rm\, km^{-1}\,s$, we find inhomogeneous reionisation does not introduce any significant bias in thermal parameter recovery for the current measurement uncertainties of $\sim 10$ per cent. However, for $5$ per cent uncertainties, $\sim 1σ$ shifts between the estimated and true parameters occur.

astro-ph.CO↗
arXiv2021

Chasing the Tail of Cosmic Reionization with Dark Gap Statistics in the Ly$α$ Forest over $5 < z < 6$

We present a new investigation of the intergalactic medium (IGM) near the end of reionization using "dark gaps" in the Lyman-alpha (Ly$α$) forest. Using spectra of 55 QSOs at $z_{\rm em}>5.5$, including new data from the XQR-30 VLT Large Programme, we identify gaps in the Ly$α$ forest where the transmission averaged over 1 comoving $h^{-1}\,{\rm Mpc}$ bins falls below 5%. Nine ultra-long ($L > 80~h^{-1}\,{\rm Mpc}$) dark gaps are identified at $z<6$. In addition, we quantify the fraction of QSO spectra exhibiting gaps longer than $30~h^{-1}\,{\rm Mpc}$, $F_{30}$, as a function of redshift. We measure $F_{30} \simeq 0.9$, 0.6, and 0.15 at $z = 6.0$, 5.8, and 5.6, respectively, with the last of these long dark gaps persisting down to $z \simeq 5.3$. Comparing our results with predictions from hydrodynamical simulations, we find that the data are consistent with models wherein reionization extends significantly below redshift six. Models wherein the IGM is essentially fully reionized that retain large-scale fluctuations in the ionizing UV background at $z \lesssim 6$ are also potentially consistent with the data. Overall, our results suggest that signature of reionization in the form of islands of neutral hydrogen and/or large-scale fluctuations in the ionizing background remain present in the IGM until at least $z \simeq 5.3$.

astro-ph.CO↗
arXiv2021

Implications of the $z>5$ Lyman-$α$ forest for the 21-cm power spectrum from the epoch of reionization

Our understanding of the intergalactic medium at redshifts $z=5$-$6$ has improved considerably in the last few years due to the discovery of quasars with $z>6$ that enable Lyman-$α$ forest studies at these redshifts. A realisation from this has been that hydrogen reionization could end much later than previously thought, so that large "islands" of cold, neutral hydrogen could exist in the IGM at redshifts $z=5$-$6$. By using radiative transfer simulations of the IGM, we consider the implications of the presence of these neutral hydrogen islands for the 21-cm power spectrum signal and its potential detection by experiments such as HERA, SKA, LOFAR, and MWA. In contrast with previous models of the 21-cm signal, we find that thanks to the late end of reionization the 21-cm power in our simulation continues to be as high as $Δ^2_{21}=10~\mathrm{mK}^2$ at $k\sim 0.1~h/$cMpc at $z=5$-$6$. This value of the power spectrum is several orders of magnitude higher than that in the conventional models considered in the literature for these redshifts. Such high values of the 21-cm power spectrum should be detectable by HERA and SKA1-LOW in $\sim 1000$ hours, assuming optimistic foreground subtraction. This redshift range is also attractive due to relatively low sky temperature and potentially greater abundance of multiwavelength data.

astro-ph.CO↗
arXiv2021

The detectability of strong 21 centimetre forest absorbers from the diffuse intergalactic medium in late reionisation models

A late end to reionisation at redshift $z\simeq 5.3$ is consistent with observed spatial variations in the Ly$α$ forest transmission and the deficit of Ly$α$ emitting galaxies around extended Ly$α$ absorption troughs at $z=5.5$. In this model, large islands of neutral hydrogen should persist in the diffuse intergalactic medium (IGM) until $z\simeq 6$. We use a novel, hybrid approach that combines high resolution cosmological hydrodynamical simulations with radiative transfer to predict the incidence of strong 21 cm forest absorbers with optical depths $τ_{21}>10^{-2}$ from the diffuse IGM in these late reionisation models. We include the effect of redshift space distortions on the simulated 21 cm forest spectra, and treat the highly uncertain heating of the pre-reionisation IGM by soft X-rays as a free parameter. For a model with only modest IGM pre-heating, such that average gas kinetic temperatures in the diffuse IGM remain below $T_{\rm K}\simeq 10^{2} \rm\, K$, we find that strong 21 cm forest absorption lines should persist until $z=6$. For a sample of $\sim 10$ sufficiently radio loud background sources, a null-detection of 21 cm forest absorbers at $z\simeq 6$ with SKA1-low or possibly LOFAR should provide an informative lower limit on the still largely unconstrained soft X-ray background at high redshift and the temperature of the pre-reionisation IGM.

astro-ph.CO↗
arXiv2021

Lyman-$α$ coupling and heating at Cosmic Dawn

The global 21-cm signal from the cosmic dawn is affected by a variety of heating and cooling processes. We investigate the impact of heating due to Lyman-$α$ (Ly~$α$) photons on the global 21-cm signal at cosmic dawn using an analytical expression of the spectrum around the Ly~$α$ resonance based on the so-called `wing approximation'. We derive a new expression for the scattering correction and for the first time give a simple close-form expression for the cooling due to injected Ly~$α$ photons. We perform a short parameter study by varying the Ly~$α$ background intensity by four orders of magnitude and establish that a strong Ly~$α$ background is necessary, although not sufficient, in order to reproduce the recently detected stronger-than-expected 21-cm signal by the EDGES Collaboration. We show that the magnitude of this Ly~$α$ heating is smaller than previously estimated in the literature by two orders of magnitude or more. As a result, even a strong Ly~$α$ background is consistent with the EDGES measurement. We also provide a detailed discussion on different expressions of the Ly~$α$ heating rate used in the literature.

astro-ph.CO↗
arXiv2021

$\mathbb{A}^1$-connected components of classifying spaces and purity for torsors

In this paper, we study the Nisnevich sheafification $\mathcal{H}^1_{\acute{e}t}(G)$ of the presheaf associating to a smooth scheme the set of isomorphism classes of $G$-torsors, for a reductive group $G$. We show that if $G$-torsors on affine lines are extended, then $\mathcal{H}^1_{\acute{e}t}(G)$ is homotopy invariant and show that the sheaf is unramified if and only if Nisnevich-local purity holds for $G$-torsors. We also identify the sheaf $\mathcal{H}^1_{\acute{e}t}(G)$ with the sheaf of $\mathbb{A}^1$-connected components of the classifying space ${\rm B}_{\acute{e}t}G$. This establishes the homotopy invariance of the sheaves of components as conjectured by Morel. It moreover provides a computation of the sheaf of $\mathbb{A}^1$-connected components in terms of unramified $G$-torsors over function fields whenever Nisnevich-local purity holds for $G$-torsors.

math.AG↗
arXiv2021

Prospects for Observing the low-density Cosmic Web in Lyman-alpha Emission

Mapping the intergalactic medium (IGM) in Lyman-$α$ emission would yield unprecedented tomographic information on the large-scale distribution of baryons and potentially provide new constraints on the UV background and various feedback processes relevant to galaxy formation. Here, we use a cosmological hydrodynamical simulation to examine the Lyman-$α$ emission of the IGM due to collisional excitations and recombinations in the presence of a UV background. We focus on gas in large-scale-structure filaments in which Lyman-$α$ radiative transfer effects are expected to be moderate. At low density the emission is primarily due to fluorescent re-emission of the ionising UV background due to recombinations, while collisional excitations dominate at higher densities. We discuss prospects of current and future observational facilities to detect this emission and find that the emission of filaments of the cosmic web will typically be dominated by the halos and galaxies embedded in them, rather than by the lower density filament gas outside halos. Detecting filament gas directly would require a very long exposure with a MUSE-like instrument on the ELT. Our most robust predictions that act as lower limits indicate this would be slightly less challenging at lower redshifts ($z \lesssim 4$). We also find that there is a large amount of variance between fields in our mock observations. High-redshift protoclusters appear to be the most promising environment to observe the filamentary IGM in Lyman-$α$ emission.

astro-ph.GA↗
arXiv2021

Revised estimates of CMB $B$-mode polarization induced by patchy reionization

The search for primordial gravitational waves through the $B$-mode polarization pattern in the CMB is one of the major goals of current and future CMB experiments. Besides foregrounds, a potential hurdle in this search is the anisotropic secondary $B$-mode polarization generated by the scattering of CMB photons off free electrons produced during patchy cosmological reionization. Robust predictions of these secondary anisotropies are challenging because of uncertainties in the reionization history. In this paper, we revise estimates of the reionization-induced $B$-mode signal by incorporating recent advances in the understanding of reionization through observations of the Lyman-$α$ forest. To derive these $B$-mode estimates, we use high-dynamic-range radiative transfer simulations of reionization that are calibrated to the Ly$α$ data. These simulations are also consistent with a variety of other high-redshift observations. We find that around multipoles $\ell\approx 100$, reionization induces $B$-mode power with $\ell(\ell+1)C_\ell^{BB}/2π\approx 4\times 10^{-6}\,μ$K$^2$. This secondary signal is thus at the level of the primordial signal with the tensor-to-scalar ratio $r<10^{-4}$, and can increase by a factor of $\sim 50$ if reionization is sourced by highly clustered sources residing in haloes with mass of $\sim 10^{11}$ M$_\odot$. Our findings suggest that the contribution of patchy reionization to the search for primordial gravitational waves is unlikely to be a concern for currently planned CMB experiments.

astro-ph.CO↗
arXiv2021

The correlation of high-redshift galaxies with the thermal Sunyaev-Zel'dovich effect traces reionization

We explore a potential new probe of reionization: the cross-correlation of high-redshift galaxies with maps of the thermal Sunyaev-Zel'dovich (tSZ) effect. We consider two types of high redshift galaxies: Lyman break galaxies (LBGs) and Lyman-$α$ emitters (LAEs). LBGs and LAEs will be detected in large numbers at high redshift ($z \approx$ 4 to 7) by ongoing and future surveys. We consider a LBG sample like that expected from the The Rubin Observatory Legacy Survey of Space and Time (LSST), and a selection of LAEs modelled after the Subaru SILVERRUSH program, but covering a much larger sky fraction. The tSZ effect is sensitive to a line-of-sight integral of the ionized gas pressure, and can be measured across large patches of the sky using multi-frequency CMB surveys. We consider forecast tSZ maps from CMB Stage 4 and more futuristic observations. Using a suite of hydrodynamical simulations, we show that the high-redshift galaxies are correlated with the tSZ signal from reionization, with cross-power amplitude of order $10^{-15}$ at $\ell \sim 1000$. The cross-spectra between LBGs/LAEs with tSZ maps contain information about the reionization history of the Universe, such as the distribution of bubble sizes, and could in principle be used to directly measure the timing of reionization. The amplitude of the signal is small, however, and its detectability is hindered by low-redshift contributions to tSZ maps and by instrumental noise. If the the low-redshift contribution to the observed tSZ signal is suppressed by masking of massive halos, a combination of overlapping futuristic CMB and galaxy surveys could potentially probe this signal.

astro-ph.CO↗
arXiv2020

Constraining the second half of reionization with the Lyman-$β$ forest

We present an analysis of the evolution of the Lyman-series forest into the epoch of reionization using cosmological radiative transfer simulations in a scenario where reionization ends late. We explore models with different midpoints of reionization and gas temperatures. We find that once the simulations have been calibrated to match the mean flux of the observed Lyman-$α$ forest at $4 < z < 6$, they also naturally reproduce the distribution of effective optical depths of the Lyman-$β$ forest in this redshift range. We note that the tail of the largest optical depths that is most challenging to match corresponds to the long absorption trough of ULAS J0148+0600, which we have previously shown to be rare in our simulations. We consider the evolution of the Lyman-series forest out to higher redshifts, and show that future observations of the Lyman-$β$ forest at $z>6$ will discriminate between different reionization histories. The evolution of the Lyman-$α$ and Lyman-$γ$ forests are less promising as a tool for pushing studies of reionization to higher redshifts due to the stronger saturation and foreground contamination, respectively.

astro-ph.CO↗
arXiv2020

Phase matching in $β$-barium borate crystals for spontaneous parametric down-conversion

Spontaneous parametric down-conversion (SPDC) is the most widely used process for generating entangled photon pairs. In SPDC, a pump photon interacts with a nonlinear optical crystal and splits into two entangled photons called the signal and the idler photons. The SPDC process has been studied extensively in the last few decades for various pump and crystal configurations, and the entangled photon pairs produced by SPDC have been used in numerous experimental studies on quantum entanglement and entanglement-based real-world quantum-information applications. In this tutorial article, we present a thorough study of phase matching in $β$-barium borate (BBO) crystals for spontaneous parametric down-conversion and thereby also investigate the generation of entangled photons in such crystals. First, we present a theoretical derivation of two-photon wavefunction produced by SPDC in the frequency and transverse momentum bases. We then discuss in detail the effects due to various crystal and pump parameters including the length of the crystal, the angle between the optic axis and the pump propagation direction, the pump incidence angle on the crystal surface, the refraction at the crystal surfaces, and the pump propagation direction inside the crystal. These effects are extremely relevant in experimental situations. We then present our numerical and experimental results in order to illustrate how various experimental parameters affect the phase matching and thus the generation of entangled photons. Finally, using the two-photon wavefunction in the transverse wave-vector basis, we show how to derive the two-photon wavefunction in the OAM basis and thereby calculate the two-photon angular Schmidt spectrum. We expect this article to be useful for researchers working in various capacities with entangled photons generated by SPDC in BBO crystals.

physics.optics↗
arXiv2020

Measurement of pure states of light in the orbital-angular-momentum basis using nine multipixel image acquisitions

The existing techniques for measuring high-dimensional pure states of light in the orbital angular momentum (OAM) basis either involve a large number of single-pixel data acquisitions and substantial postselection errors that increase with dimensionality, or involve substantial loss, or require interference with a reference beam of known phase. Here, we propose an interferometric technique that can measure an unknown pure state using only nine multipixel image acquisitions without involving postselection, loss, or a separate reference beam. The technique essentially measures two complex correlation functions of the input field and then employs a recursive postprocessing algorithm to infer the state. We experimentally demonstrate the technique for pure states up to dimensionality of 25, reporting a mean fidelity greater than 90 % up to 11 dimensions. Our technique can significantly improve the performance of OAM-based information processing applications.

physics.optics↗
arXiv2020

Probing the thermal state of the intergalactic medium at $z>5$ with the transmission spikes in high-resolution Ly$α$ forest spectra

We compare a sample of five high-resolution, high S/N Ly$α$ forest spectra of bright $6 5$ with those obtained from mock absorption spectra from the Sherwood and Sherwood-Relics suites of hydrodynamical simulations of the intergalactic medium (IGM). We use a profile fitting procedure for the inverted transmitted flux, $1-F$, similar to the widely used Voigt profile fitting of the transmitted flux $F$ at lower redshifts, to characterise the transmission spikes that probe predominately underdense regions of the IGM. We are able to reproduce the width and height distributions of the transmission spikes, both with optically thin simulations of the post-reionization Universe using a homogeneous UV background and full radiative transfer simulations of a late reionization model. We find that the width of the fitted components of the simulated transmission spikes is very sensitive to the instantaneous temperature of the reionized IGM. The internal structures of the spikes are more prominant in low temeperature models of the IGM. The width distribution of the observed transmission spikes, which require high spectral resolution ($\leq $ 8 km/s) to be resolved, is reproduced for optically thin simulations with a temperature at mean density of $T_0= (11000 \pm 1600,10500\pm 2100,12000 \pm 2200)$ K at $z= (5.4,5.6,5.8)$. This is weakly dependent on the slope of the temperature-density relation, which is favoured to be moderately steeper than isothermal. In the inhomogeneous, late reionization, full radiative transfer simulations where islands of neutral hydrogen persist to $z\sim5.3$, the width distribution of the observed transmission spikes is consistent with the range of $T_0$ caused by spatial fluctuations in the temperature-density relation.

astro-ph.CO↗
arXiv2020

Probing delayed-end reionization histories with the 21cm-LAE cross-power spectrum

We model the 21-cm signal and LAE population evolution during the epoch of reionization in order to predict the 21cm-LAE cross-power spectrum. We employ high-dynamic-range simulations of the IGM to create models that are consistent with constraints from the CMB, Lyman-$α$ forest and LAE population statistics. Using these models we consider the evolution of the cross-power spectrum for a selection of realistic reionization histories and predict the sensitivity of current and upcoming surveys to measuring this signal. We find that the imprint of a delayed-end to reionization can be observed by future surveys, and that strong constraints can be placed on the progression of reionization as late as $z=5.7$ using a Subaru-SKA survey. We make predictions for the signal-to-noise ratios achievable by combinations of Subaru/PFS with the MWA, LOFAR, HERA and SKA interferometers for an integration time of 1000 hours. We find that a Subaru-SKA survey could measure the cross-power spectrum for a late reionization at $z=6.6$ with a total signal-to-noise greater than 5, making it possible to constrain both the timing and bubble size at the end of reionization. Furthermore, we find that expanding the current Subaru/PFS survey area and depth by a factor of three would double the total signal-to-noise.

astro-ph.CO↗
arXiv2020

Intrinsic degree of coherence of two-qubit states and measures of two-particle quantum correlations

Recently, a basis-invariant measure of coherence known as the intrinsic degree of coherence has been established for classical and single-particle quantum states [JOSA B {\bf 36}, 2765 (2019)]. Using the same mathematical construction, in this article, we define the intrinsic degree of coherence of two-qubit states and demonstrate its usefulness in quantifying two-particle quantum correlations and entanglement. In this context, first of all, we show that the intrinsic degree of coherence of a two-qubit state puts an upper bound on the violations of Bell inequalities that can be achieved with the state and that a two-qubit state with intrinsic degree of coherence less than $1/\sqrt{3}$ cannot violate Bell inequalities. We then show that the quantum discord of a two-qubit state, which quantifies the amount of quantum correlations available in the two-qubit state for certain tasks, is bounded from above by the intrinsic degree of coherence of the state. Next, in the context of two-particle entanglement, we show that the range of values that the concurrence of a two-qubit state can take is decided by the intrinsic degree of coherence of the two-qubit state together with that of the individual qubits. Finally, for the polarization two-qubit states generated by parametric down-conversion of a pump photon, we propose an experimental scheme for measuring the intrinsic degree of coherence of two-qubit states. We also present our theoretical study showing how the intrinsic degree of coherence of a pump photon dictates the maximum intrinsic degree of coherence of the generated two-qubit state.

quant-ph↗