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We carry out the first investigation of the entanglement and mutual information harvesting protocols for detectors moving on freely falling trajectories that cross the horizon of a black hole. We consider two pointlike Unruh-DeWitt detectors in different combinations of free-falling and static trajectories in (1+1)-dimensional Schwarzschild black hole spacetime and compare the results. We find that (i) correlations harvested between free-falling and static detectors are always less than those of the familiar two-static-detector case (ii) there is a large kinematic component to the correlations; (ii) correlations can be harvested purely from the quantum vacuum, with evidence that this is possible even when the detectors are causally disconnected by the event horizon; (iii) the previously known `entanglement shadow&#39; near the horizon is indeed absent for the two free-falling-detector case since the relative gravitational redshift of the detectors remains finite as the horizon is crossed, in accordance with the equivalence principle.

CAP Virtual Congress 2021

Harvesting Entanglement inside a Black Hole

unruh-dewitt detectors

schwarzschild black hole

relativistic quantum information

entanglement harvesting

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We carry out the first investigation of the entanglement and mutual information harvesting protocols for detectors moving on freely falling trajectories that cross the horizon of a black hole. We consider two pointlike Unruh-DeWitt detectors in different combinations of free-falling and static trajectories in (1+1)-dimensional Schwarzschild black hole spacetime and compare the results. We find that (i) correlations harvested between free-falling and static detectors are always less than those of the familiar two-static-detector case (ii) there is a large kinematic component to the correlations; (ii) correlations can be harvested purely from the quantum vacuum, with evidence that this is possible even when the detectors are causally disconnected by the event horizon; (iii) the previously known `entanglement shadow' near the horizon is indeed absent for the two free-falling-detector case since the relative gravitational redshift of the detectors remains finite as the horizon is crossed, in accordance with the equivalence principle.

technical paper

Magnetic Resonance Imaging (MRI) detects signal from hydrogen nuclei in biological tissue. MRI requires a homogeneous static magnetic field to generate artifact-free images. The subject is spatially encoded with magnetic field gradients. The signal is acquired in the frequency domain and the image is reconstructed by inverse Fourier transform. Objects with high magnetic susceptibility, such as MRI-safe metallic implants, distort the surrounding magnetic field. This leads to severe artifacts that appear as signal voids in the conventional MRI images, due to rapid intravoxel dephasing, in addition to misregistration of frequencies to position.
Pure phase encoding techniques with short encoding times are largely immune to magnetic field inhomogeneity artifacts. This is because the constant signal evolution times can be sufficiently short that no appreciable dephasing has occurred. High quality artifact-free MRI images were acquired with pure phase encoding techniques, from which the magnetic field distribution around the metal was derived. This approach was compared with conventional MRI methods, which failed to map the magnetic field in high susceptibility regions. Although it is challenging to apply the proposed method in a routine clinical MRI scan, the measured magnetic field distribution could enable the development of novel nonlinear encoding techniques, where the metal induced magnetic field distortion is exploited to provide spatial information.

Mapping Magnetic Field Around Metal with Pure Phase Encoding Magnetic Resonance Imaging

Calcium (Ca) is an essential mineral in the body that helps maintain healthy bone density. Dysreguation of Ca can result in serious health issues and a reliable and efficient method of identifying changes in bone mineral balance can help to provide eaarly diagnosis of deteriorating bone health. The objective of this project is to investigate the application of naturally occurring Ca isotope abundance variations to understand biological processes, including biomineralization. This is because the kinetics underlying metabolic processes that involve Ca are mass dependent and will redistribute the abundances of naturally occuring, stable Ca isotopes. Thus, a careful measurement of Ca isotopic composition of the Ca pools in the body (i.e. bone, blood, and urine) can provide unique insight into the disruption of Ca metabolism. The extent of natural variations of stable Ca isotopes in the human metabolism is limited with a relative natural variation of less than 0.5% in the 44Ca/40Ca isotope amount ratio. Therefore, reliable measurement of Ca isotopic composition has remained very challenging, especially considering low Ca levels and significant procedural blank levels. The goal of this project was so develop a reliable and accurate analytical measurement procedures specifically for small amounts (approx. 1 µg) of Ca in biological materials.

In this study the extraction and isolation of calcium from a diverse set of biological matrices was optimized for low procedural blanks and separation from matrix elements and isobaric interferences such as Na, Mg, K, Mg, Ti, Fe, Ba. A 42Ca–48Ca double spike (DS) was applied to correct for potential isotopic fractionation during sample preparation and measurement. Ca isotope abundance analysis was performed using a multicollector thermal ionization mass spectrometer. The measurement procedure enabled processing of total Ca amounts of 1000 ng, with a total procedural blank of <10 ng and enabled measurement of the Ca isotopic compositions of the reference materials NIST SRM 1400 (bone ash), NIST SRM 1486 (bone meal) and IAPSO (seawater).

Dorothy Walls1, Anika Retzmann2, Kerri A. Miller1, Johanna Irrgeher1,2, Thomas Prohaska1,2, Michael Wieser1

1 Department of Physics and Astronomy, University of Calgary, Canada.

2 Chair of General and Analytical Chemistry, Montanuniversität Leoben, Austria.

Measuring calcium isotopic composition in the body to understand metabolic processes.

In the case of binary black hole mergers, the surface of most obvious interest, the Event Horizon, is often computationally difficult to locate. Instead, it is useful to turn to quasi-local characterizations of black hole boundaries, such as Marginally Outer Trapped Surfaces (MOTS), which are defined for a single time slice of the spacetime, and the outer-most of which is the apparent horizon. In this talk, I will describe ongoing work focused on understanding MOTS in the interior of a five-dimensional black hole; both static and rotating. Similar to the four-dimensional Schwarzschild case previously studied, we find examples of self-intersecting MOTS with an arbitrary number of self-intersections. This provides further support that self-intersecting behavior is rather generic. I will also discuss the second stage of our research, which is for a rotating 5D black hole spacetime. These two cases fit into a larger project involving exploration of the generality of self-intersecting behaviour in MOTS, within spacetimes of increasing diversity.

Marginally Outer Trapped (Open) Surfaces in 4+1 Dimensional Spacetimes

**Introduction:** pHi is a hallmark of altered cellular function in the tumour microenvironment and its response to therapies. One of the main acid-extruding membrane transport proteins in cells is the Na+/H+ exchanger isoform 1 (NHE1). Chemical exchange saturation transfer (CEST) MRI uniquely images pHi. In CEST-MRI, contrast is produced by exciting exchangeable tissue protons at their specific absorption frequency and observing the transfer of magnetization to bulk tissue water. Amine and amide concentration-independent detection (AACID) is a ratiometric approach that uses the distinctive sensitivity of amine and amide protons to CETS contrast. The AACID value inversely relates to tissue pHi. One way to achieve tumour acidification as a therapeutic strategy is by blocking the NHE1 transporter. Cariporide is a potent inhibitor of NHE1. We have shown that cariporide can selectively acidify U87MG glioma in mice. The goal of this study was to determine whether cariporide also selectively acidifies a rat C6 glioma tumour model immediately following injection by mapping tumour pHi.
**Methods:** A 2μL suspension of 10^6 C6 glioma cells were injected into the right frontal lobe of six 8-week-old male rats. To evaluate the effect of cariporide on tumour pHi, rats received an IP injection of the drug (6mg/kg in 2ml) two weeks after tumour implantation. They received the drug inside a 9.4T scanner to measure the change in pHi following injection. 
**Results:** Five minutes after injection we started collecting CEST-MRI for 3 hours. For data analysis, we compared the first maximum change in AACID value post-injection with the pre-injection value. Approximately 60 minutes after injection, the average AACID value in the tumour significantly increased (p<0.05). The average AACID value in tumour post-injection was 5.4% higher compared to pre-injection corresponding to a 0.26 lower pHi. The average AACID value in contralateral tissue also increased in a similar way.
**Conclusion:** We did not observe selective tumour acidification following injection as was observed in the previous study. The reason for this discrepancy is currently unknown but may be related to potential differences in tumour vasculature that may limit the ability of cariporide to infiltrate the tumour. Future work includes increasing cariporide dose and modifying our quantification method to increase the temporal stability of the AACID measurement.

Cariporide Effects on Intracellular pH (pHi) Using CEST-MRI in Rat Model of Glioblastoma

Graphene field effect transistors (GFETs) have an enormous potential for the development of next-generation gas sensors, but more efforts are required to improve their sensitivity and selectivity. In this talk we discuss UV illumination as a promising method to enhance the performance of GFETs for the detection and recognition of analytes such as ethanol, water vapor and dimethyl methylphosphonate (DMMP), a molecule with structural similarities to nerve agents such as sarin. We show that illuminating the devices in operando with a UV LED results in both improved sensitivity and selectivity. By monitoring the sensing response of the GFETs as a function of gate voltage, we directly demonstrate that a shift in the Dirac point due to the optical doping is associated with the increased sensitivity. Moreover, we discuss how the substrate and fabrication residues on the surface of the graphene sensors can play a role in modifying the sensing performance.

Optically enhanced gas sensing performance of graphene field effect transistors

High harmonic generation (HHG) in gasses has become a method of choice among table-top extreme ultraviolet (XUV) sources. In order to generate higher photon energies from this process, many strategies can be implemented, including red-shifting and compressing the driver pulses. Here, we propose a new approach for inducing a red-shift to driver pulses and compressing them to few-cycle durations in a single stage. This method uses the recently discovered multidimensional solitary states (MDSS) pulses that result from the nonlinear Raman process in gas-filled hollow-core fibers. It has a few key advantages: 1) MDSS are created from relatively long pulses, making this method suitable for any laser source offering sub-picosecond pulses. 2) The MDSS pulses can be compressed by simple propagation through glass. 3) In contrast with commonly-used optical parametric amplifiers, the induced red-shift can be modest, allowing to reach a target XUV photon energy while minimizing the detrimental effects of long driver wavelengths on HHG efficiency. 
To produce MDSS pulses, the output pulses of a Titanium-Sapphire system are stretched to 400 fs and coupled to a hollow-core fiber filled with nitrogen. In the fiber, intermodal nonlinear processes occur which lead to the red-shifted MDSS pulses. Then, CaF2 plates inserted into the beam path compress the pulses down to 12 fs and these are sent to an argon-filled cell where HHG occurs. From this simple apparatus, the HHG spectrum is expanded to cover the M$_{2,3}$ edge of cobalt and $10^9$ photons/second are generated at 60 eV. This significant XUV photon flux allows for the implementation of X-ray resonant magnetic scattering measurements on a cobalt/platinum ferromagnet, an example of photon-hungry application. Although such flux has previously been generated in a different gas from the direct output of the same laser system, the conversion efficiency of our approach is one order of magnitude higher as it allows to reach the target photon energy by generating harmonics in argon, a gas that offers a large generation efficiency. Due to its simplicity and versatility, our approach can readily be adapted to different applications and could be particularly interesting for high power Ytterbium laser systems offering sub-picosecond pulses.

Multidimensional Raman Solitons as Drivers of the High Harmonic Generation Process

Seawater spray and precipitation are two main sources of icing and ice accumulation in cold ocean regions, presenting a major challenge for shipping and operating maritime equipment [1]. 
There is a limited number of analytical techniques to study seawater spray ice formation. MRI is known for its non-invasive capabilities in measurements of a solid ice [2,3]. In this work, we investigated the potential of MRI as an analytical measurement technique for studies of the seawater spray ice. 
The signal detected with MRI/NMR comes from pockets of brine in the forming ice, and the unfrozen water, with the 1H NMR signal from the brine decreasing as the temperature drops and the brine freezes further. 3D MRI showed different freezing patterns and temperature gradients depending on the initial freezing temperature and the surface geometry. T1-T2 maps indicated strong changes in relaxation parameters as the freezing progresses, indicating changing environment for the brine in the growing ice [4]. In a separate freezing series using Na NMR, the amount of sodium in the brine remained almost unchanged until the brine reached the eutectic temperature, and the sodium precipitation accelerated.
These measurements were done on an MRI scanner, with the freezing setup designed to fit a 4 cm i.d. RF probe inside a 2.4 T superconducting magnet. To explore a possibility of using NMR for freezing studies in a more open environment, we also used a portable, unilateral NMR device to characterize sea spray freezing on a cold surface. The device consisted of a flat 3-magnet array [5] with the sensitive volume (approx.2 mm x 15 x 15 mm) at 1 cm away from the magnet surface. 1D-resolved 1H NMR measurements provided information on the brine concentration, T2 and diffusion at a range of temperatures.
The results provide information on the changing environment in brine in freezing sea sprays, with a potential for NMR studies both in the lab and in the field.

[1]A.R. Dehghani-Sanij, S.R. Dehghani, G.F. Naterer, Y.S. Muzychka, Ocean Eng. 143 (2017) 1–23.
[2]M.W. Hunter, R. Dykstra, M.H. Lim, T.G. Haskell, P.T. Callaghan, Appl. Magn. Reson. 36 (2009) 1–8.
[3]J.R. Brown, T.I. Brox, S.J. Vogt, J.D. Seymour, M.L. Skidmore, S.L. Codd, J. Magn. Reson. 225 (2012) 17–24. 
[4] G.Wilbur, B.MacMillan, K.M.Bade, I.Mastikhin, J. Magn. Reson. 310 (2020) 106647.
[5] J.C.Garcia-Naranjo, I.Mastikhin, B.J.Colpitts, B.J.Balcom, J. Magn.Reson. 207 (2010) 337-344

Sea spray freezing measurements with MRI and portable NMR

Gravitational Wave (GW) detection from continuous sources such as pulsars is an anticipated discovery. However, due to exceedingly weak signals, detection is challenging. In this presentation, we detail the derivation of a Fourier transform of a continuous wave signal amenable for detection of the GW signal from a pulsar. We also present an easy to implement algorithm for computing peak heights and frequencies from analytical results arising from features in frequency evolution of gravitational wave signals. Our approach can handle gaps in data, allowing longer
coherence lengths. While the presentation focuses on GW detection from pulsar, our results are general and can be applied to any monochromatic signals of this form.

Fourier transform of gravitational wave signals from a pulsar

In optics, caustics are bright, sharp lines and shapes created by the natural focusing of light. Some examples include rainbows, the wavy lines on the bottom of swimming pools and the patterns produced by gravitational lensing. The intensity at a caustic diverges in the classical ray theory, but can be smoothed by taking into account the wave nature of light. In this work we consider a new type of caustic that occurs in quantum systems due to phase singularities; because phase is such a central concept in wave theory, this heralds the breakdown of the wave description and is an example of a quantum caustic. In particular, we consider analogue black holes which can be formed in a flowing Bose-Einstein condensate (BEC) gas. Waves flowing near the event horizon (describing analogue Hawking radiation) appear to suffer a logarithmic phase divergence, which is known as the trans-Planckian problem for gravitational black holes. We describe the regularization procedure required to cure this quantum caustic in our BEC system, and make connections to catastrophe theory.

Hawking radiation as a quantum caustic

Purpose: A quantitative measure of delivered ionizing radiation is recommended for quality assurance and quality control purposes for patients undergoing radiotherapy treatments. Current dosimeters are not well suited for direct measurements due to atomic composition and size limitations. We are developing a fiber optic probe dosimeter based on radiochromic material for in vivo dosimetry. Through measuring the change in optical absorption of the radiochromic sensor, we can quantify the absorbed dose of ionization radiation delivered in real-time. The radiation-sensitive material is composed of lithium-10,12-pentacosa diynoate (LiPCDA), which upon exposure, polymerizes and results in an increased optical density. We observed that monomers of LiPCDA can have two distinct crystalline morphologies, with aspect ratios 10:1 producing hair-like structures and 2:1 resulting in platelets, with polymerized absorbance peaks typically centred at 635 nm and 674 nm, respectively. We aim to characterize and compare the dose-response of the two crystal morphologies achieved through desiccation and Li+ concentration. 

Method: The hair-like LiPCDA in commercial film was desiccated, producing crystals with an absorbance peak at 674 nm. Both materials were exposed to 50-3000 cGy using a clinical linear accelerator with a 6MV X-ray beam; samples of varying Li+ concentration were exposed to 200-400 cGy. Absorbance spectra for all samples were collected and were imaged with a scanning electron microscope to compare their crystal morphology. 

Results: Differences in crystal morphology were not observed when hair-like LiPCDA was desiccated. However, varying the molar ratio of Li+ to PCDA to produce crystals with either 635 nm or 677 nm absorbance peak, differentiable crystal morphologies were observed. The platelet form is ~3x less sensitive to dose but with a more extensive dynamic range relative to hair-like. 

Conclusion: Crystals can be preferentially grown and exhibit differing dose-response. The macrostructure effect on radiation sensitivity in the context of radiotherapy will be explored.

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