We investigate the importance of going beyond the mean-field approximation in the dynamics of collective neutrino oscillations. To expand our understanding of the coherent neutrino oscillation problem, we apply concepts from many-body physics and quantum information theory. Specifically, we use measures of nontrivial correlations (otherwise known as "entanglement") between the constituent neutrinos of the many-body system, such as the entanglement entropy and the Bloch vector of the reduced density matrix. The relevance of going beyond the mean field is demonstrated by comparisons between the evolution of the neutrino state in the many-body picture vs the mean-field limit, for different initial conditions.
Extreme conditions present in the interiors of the core-collapse supernovae make neutrino-neutrino interactions not only feasible but dominant in specific regions, leading to the non-linear evolution of the neutrino flavor. Results obtained when such collective neutrino oscillations are treated in the mean-field approximation deviate from the results using the many-body picture because of the ignored quantum correlations. We present the first three flavor many-body calculations of the collective neutrino oscillations. The entanglement is quantified in terms of the entanglement entropy and the …
In an interacting neutrino gas, flavor coherence becomes dynamical and can propagate as a collective mode. In particular, tachyonic instabilities can appear, leading to "fast flavor conversion" that is independent of neutrino masses and mixing angles. On the other hand, without neutrino-neutrino interaction, a prepared wave packet of flavor coherence simply dissipates by kinematical decoherence of infinitely many non-collective modes. We reexamine the dispersion relation for fast flavor modes and show that for any wavenumber,there exists a continuum of non-collective modes besides a few discre…
We give a very brief overview of collective effects in neutrino oscillations in core collapse supernovae where refractive effects of neutrinos on themselves can considerably modify flavor oscillations, with possible repercussions for future supernova neutrino detection. We discuss synchronized and bipolar oscillations, the role of energy and angular neutrino modes, as well as three-flavor effects. We close with a short summary and some open questions.
We investigate the multi-azimuthal angle (MAA) effect on collective neutrino oscillation by considering the three-dimensional neutrino momentum distribution in a realistic electron-capture supernova model with an $8.8 M_{\odot}$ progenitor. We find that the MAA effect induces collective flavor conversions at epochs when it is completely suppressed under the axial-symmetric approximation. This novel activity is switched on/off by the growth of the MAA instability and imprints additional time evolution in the expected neutrino event rate. We validate our results by extending the linear stability…
We demonstrate the non-negligible effect of transition magnetic moments on three-flavor collective oscillations of Majorana neutrinos in the core of type-II supernovae, within the single-angle approximation. We argue that data from a galactic supernova in conjunction with terrestrial experiments can potentially give us clues about the non-zero nature of neutrino transition magnetic moments if these are Majorana fermions, even if their values are as small as those predicted by the Standard Model augmented by nonzero neutrino Majorana masses.
In environments such as core-collapse supernovae, neutron star mergers, or the early universe, where the neutrino fluxes can be extremely high, neutrino-neutrino interactions are appreciable and contribute substantially to their flavor evolution. Such a system of interacting neutrinos can be regarded as a quantum many-body system, and prospects for nontrivial quantum correlations, i.e., entanglement, developing in a gas of interacting neutrinos have been investigated previously. In this work, we uncover an intriguing connection between the entropy of entanglement of individual neutrinos with t…
Localization effects and quantum decoherence driven by the mass-eigenstate wave packet propagation are shown to support a statistical correlation between quantum entanglement and damped oscillations in the scenario of three-flavor quantum mixing for neutrinos. Once the mass-eigenstates that support flavor oscillations are identified as three-{\em qubit} modes, a decoherence scale can be extracted from correlation quantifiers, namely the entanglement of formation and the logarithmic negativity. Such a decoherence scale is compared with the coherence length of damped oscillations. Damping signat…
Neutrinos and antineutrinos emitted from a core collapse supernova interact among themselves, giving rise to collective flavor conversion effects that are significant near the neutrinosphere. We develop a formalism to analyze these collective effects in the complete three-flavor framework. It naturally generalizes the spin-precession analogy to three flavors and is capable of analytically describing phenomena like vacuum/MSW oscillations, synchronized oscillations, bipolar oscillations and spectral split. Using the formalism, we demonstrate that the flavor conversions may be "factorized" into …
Neutrinos in supernovae, neutron stars, and in the early Universe may change flavor collectively and unstably, due to neutrino-neutrino forward-scattering. We prove that for collective instability to occur, the difference of momentum distributions of two flavors must change sign, i.e., there is a zero crossing. This necessary criterion, which unifies slow and fast instabilities, is valid for Hamiltonian flavor-evolution of ultra-relativistic Standard Model neutrino occupation matrices, including damping due to collisions in the relaxation approximation. It provides a simple but rigorous condit…
We calculate the correlation functions needed to describe the linear response of superfluid matter, and go on to calculate the differential cross section for neutral-current neutrino scattering in superfluid neutron matter and in color-flavor locked quark matter (CFL). We report the first calculation of scattering rates that includes neutrino interactions with both pair-breaking excitations and low-lying collective excitations (Goldstone modes). Our results apply both above and below the critical temperature, allowing use in simulations of neutrino transport in supernovae and neutron stars.
We investigate theta-vacuum effects on the QCD phase diagram for the realistic 2+1 flavor system, using the three-flavor Polyakov-extended Nambu-Jona-Lasinio (PNJL) model and the entanglement PNJL model as an extension of the PNJL model. The theta-vacuum effects make the chiral transition sharper. For large theta-vacuum angle the chiral transition becomes first order even if the quark number chemical potential is zero, when the entanglement coupling between the chiral condensate and the Polyakov loop is taken into account. We finally propose a way of circumventing the sign problem on lattice Q…
Collective neutrino oscillations play a crucial role in transporting lepton flavor in astrophysical settings, such as supernovae, where the neutrino density is large. In this regime, neutrino-neutrino interactions are important and simulations in the mean-field approximation show evidence for collective oscillations occurring at time scales much larger than those associated with vacuum oscillations. In this work, we study the out-of-equilibrium dynamics of a corresponding spin model using Matrix Product States and show how collective bipolar oscillations can be triggered by many-body correlati…
A self-consistent large $N_c$ approach is developed for the collective quantization of SU(3) flavor hedgehog solitons, such as the Skyrmion. The key to this analysis is the determination of all of the zero modes associated with small fluctuations around the hedgehog. These are used in the conventional way to construct collective coordinates. This approach differs from previous work in that it does not implicitly assume that each static zero mode is associated with a dynamical zero mode. It is demonstrated explicitly in the context of the Skyrmion that there are fewer dynamical zero modes than …
The vp process is a primary nucleosynthesis process which occurs in core collapse supernovae. An essential role in this process is being played by electron antineutrinos. They generate, by absorption on protons, a supply of neutrons which, by (n,p) reactions, allow to overcome waiting point nuclei with rather long beta-decay and proton-capture lifetimes. The synthesis of heavy elements by the vp process depends sensitively on the \barν_e luminosity and spectrum. As has been shown recently, the latter are affected by collective neutrino flavor oscillations which can swap the \barν_e and \barν_{…
A dense neutrino medium can experience collective flavor oscillations through nonlinear neutrino-neutrino refraction. To make this multi-dimensional flavor transport problem more tractable, all existing studies have assumed certain symmetries (e.g., the spatial homogeneity and directional isotropy in the early universe) to reduce the dimensionality of the problem. In this work we show that, if both the directional and spatial symmetries are not enforced in the neutrino line model, collective oscillations can develop in the physical regimes where the symmetry-preserving oscillation modes are st…
A dense neutrino medium such as that inside a core-collapse supernova can experience collective flavor conversion or oscillations because of the neutral-current weak interaction among the neutrinos. This phenomenon has been studied in a restricted, stationary supernova model which possesses the (spatial) spherical symmetry about the center of the supernova and the (directional) axial symmetry around the radial direction. Recently it has been shown that these spatial and directional symmetries can be broken spontaneously by collective neutrino oscillations. In this paper we analyze the neutrino…
(Abridged) In order to decode the neutrino burst signal from a Galactic core-collapse supernova and reveal the complicated inner workings of the explosion we need a thorough understanding of the neutrino flavor evolution from the proto-neutron star outwards. The flavor content of the signal evolves due to both neutrino collective effects and matter effects which can lead to a highly interesting interplay and distinctive spectral features. In this paper we investigate the supernova neutrino flavor evolution in three different progenitors and include collective flavor effects, the evolution of t…
Neutrino flavor evolution in core-collapse supernovae, neutron-star mergers, or the early universe is dominated by neutrino-neutrino refraction, often spawning "self-induced flavor conversion", i.e., shuffling of flavor among momentum modes. This effect is driven by collective run-away modes of the coupled "flavor oscillators" and can spontaneously break the initial symmetries such as axial symmetry, homogeneity, isotropy, and even stationarity. Moreover, the growth rates of unstable modes can be of the order of the neutrino-neutrino interaction energy instead of the much smaller vacuum oscill…
We perform numerical simulations of fast collective neutrino flavor conversions in an one-dimensional box mimicking a system with the periodic boundary condition in one spatial direction and translation symmetry in the other two dimensions. We evolve the system over several thousands of the characteristic timescale (inverse of the interaction strength) with different initial $\barν_e$ to $ν_e$ number density ratios and different initial seed perturbations. We find that small scale structures are formed due to the interaction of the flavor waves. This results in nearly flavor depolarization in …
I study the flavor evolution of a dense neutrino gas by considering vacuum contributions, matter effects and neutrino self-interactions. Assuming a system of two flavors in a uniform matter background, the time evolution of the many-body system in discretized momentum space is computed. The multi-angle neutrino-neutrino interactions are treated exactly and compared to both the single-angle approximation and mean field calculations. %The time unit chosen is $μ_0^{-1}=(\frac{G_F}{2\sqrt{2}V})^{-1}$. The mono-energetic two neutrino beam scenario is solved analytically. I proceed to solve flavor o…
We explore the effects of collective neutrino flavor oscillations due to neutrino-neutrino interactions on the neutrino heating behind a stalled core-collapse supernova shock. We carry out axisymmetric (2D) radiation-hydrodynamic core-collapse supernova simulations, tracking the first 400 ms of the post-core-bounce evolution in 11.2 solar mass and 15 solar mass progenitor stars. Using inputs from these 2D simulations, we perform neutrino flavor oscillation calculations in multi-energy single-angle and multi-angle single-energy approximations. Our results show that flavor conversions do not set…
Dense clouds of neutrinos and antineutrinos can exhibit fast collective flavor oscillations. Previously, in Phys. Rev. Lett. 126 (2021) 061302, we proposed that such flavor oscillations lead to depolarization, i.e., an irreversible mixing of the flavors, whose extent depends on the initial momentum distributions of the different flavors. In this paper, we elaborate and extend this proposal, and compare it with related results in the literature. We present an accurate analytical estimate for the lower resting point of the fast flavor pendulum and underline the relaxation mechanisms, i.e., trans…
Flavor--Kinetic Entanglement Production from Decay and Scattering at Finite Density
School of Physics, Peking University（北京大学物理学院）；State Key Laboratory of Nuclear Physics and Technology, Peking University（北京大学核物理与技术国家重点实验室）；Center for High Energy Physics, Peking University（北京大学高能物理中心）；School of Physics, Beihang University（北京航空航天大学物理学院）
Dense neutrino gases form in extreme astrophysical sites, and the flavor content of the neutrinos likely has an important impact on the subsequent dynamical evolution of their environment. Through coherent forward scattering among neutrinos, the flavor content of the gas evolves under a time-dependent potential which can be modeled in a quantum many-body formalism as an all-to-all coupled spin-spin interaction. This two-body potential generically introduces entanglement and greatly complicates the study of these systems. In this work we study the evolution of the quantum many-body problem as w…
Entanglement suppression in the strong interaction $S$-matrix is shown to be correlated with approximate spin-flavor symmetries that are observed in low-energy baryon interactions, the Wigner $SU(4)$ symmetry for two flavors and an $SU(16)$ symmetry for three flavors. We conjecture that dynamical entanglement suppression is a property of the strong interactions in the infrared, giving rise to these emergent symmetries and providing powerful constraints on the nature of nuclear and hypernuclear forces in dense matter.
Collective flavor transformations in supernovae, caused by neutrino-neutrino interactions, are essentially a two-flavor phenomenon driven by the atmospheric mass difference and the small mixing angle theta_13. In the two-flavor approximation, the initial evolution depends logarithmically on theta_13 and the system remains trapped in an unstable fixed point for theta_13 = 0. However, any effect breaking exact nu_mu-nu_tau equivalence triggers the conversion. Such three-flavor perturbations include radiative corrections to weak interactions, small differences between the nu_mu and nu_tau fluxes,…
Collective neutrino oscillations are critical to determine the neutrino flavor content, which has striking impacts on core-collapse supernovae or compact binary merger remnants. It is a challenging many-body problem that so far has been mainly studied at the mean-field approximation. We use a setup that captures the relevant physics and allows exact solution for a large number of neutrinos. We, for the first time, find quantitative deviation from the mean-field evolution due to many-body decoherence in flavor space. Similar features have been observed in a spin-1 Bose-Einstein condensate, whic…
Neutrinos emitted deep within a supernova explosion experience a self-induced index of refraction. In the stationary, one-dimensional (1D) supernova "bulb model", this self-induced refraction can lead to a collective flavor transformation which is coherent among different neutrino momentum modes. Such collective oscillations can produce partial swaps of the energy spectra of different neutrino species as the neutrinos stream away from the proto-neutron star. However, it has been demonstrated that the spatial symmetries (such as the spherical symmetry in the bulb model) can be broken spontaneou…
Neutrino and antineutrino fluxes from a core-collapse galactic supernova are studied, within a representative three-flavor scenario with inverted mass hierarchy and tiny 1-3 mixing. The initial flavor evolution is dominated by collective self-interaction effects, which are computed in a full three-family framework along an averaged radial trajectory. During the whole time span considered (t=1-20 s), neutrino and antineutrino spectral splits emerge as dominant features in the energy domain for the final, observable fluxes. Some minor or unobservable three-family features (e.g., related to the m…
In a core collapse supernova, collective oscillations of neutrinos emitted by the proto-neutron star significantly modifies the partition of energy between different flavors in a way which is potentially important for the nucleosynthesis of heavy elements at the outer layers. As the outcome of collective oscillations depends nonlinearly on the chosen initial conditions proto-neutron star, their systematical study across the proto-neutron star model space may provide answers to some key questions.
We examine coherent active-active channel neutrino flavor evolution in environments where neutrino-neutrino forward scattering can engender large-scale collective flavor transformation. We point out a key quantity, the "total effective energy", which is conserved in several important regimes. Using this concept, we analyze collective neutrino and antineutrino flavor oscillation in the "synchronized" mode and what we term the "bi-polar" mode. We thereby are able to explain why large collective flavor mixing can develop on short timescales even when vacuum mixing angles are small in, e.g., a den…
We show that the bump in the electron number density profile at the base of the hydrogen envelope in O-Ne-Mg core-collapse supernovae causes an interesting interplay between neutrino-electron and neutrino-neutrino forward scattering effects in the flavor evolution of low-energy nu_e in the neutronization burst. The bump allows a significant fraction of the low-energy nu_e to survive by rendering their flavor evolution nonadiabatic. Increasing the luminosity of the neutronization burst shifts the bump-affected nu_e to lower energy with reduced survival probability. Similarly, lowering the lumin…
We identify a generic new form of collective flavor oscillations in dense neutrino gases that amounts to a self-induced parametric resonance. It occurs in a homogeneous and isotropic ensemble when a range of neutrino modes is prepared in a different flavor than the neighboring modes with lower and higher energies. The flavor content of the intermediate spectral part librates relative to the other parts with a frequency corresponding to a typical Delta m^2/2E. This libration persists in the limit of an arbitrarily large neutrino density where one would have expected synchronized flavor oscillat…
We study three-flavor collective neutrino transformations in the dense-neutrino region above the neutrino sphere of a supernova core. We find that two-flavor conversions driven by the atmospheric mass difference and the 13-mixing angle capture the full effect if one neglects the second-order difference between the muon and tau neutrino refractive index. Including this "mu-tau matter term" provides a resonance at a density of approximately 3 x 10^7 g cm^-3 that typically causes significant modifications of the overall electron neutrino and antineutrino survival probabilities. This effect is sur…
As a result of a non-trivial mixing matrix, neutrinos cannot be simultaneously in a flavor and mass eigenstate. We formulate and discuss information entropic relations that quantify the associated quantum uncertainty. We also formulate a protocol to determine the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix from quantum manipulations and measurements on an entangled lepton-neutrino pair. The entangled state features neutrino oscillations in a conditional probability involving measurements on the lepton and the neutrino. They can be switched off by choosing a specific observable on the lepton …
In an environment with high-density neutrinos formed in a core-collapse supernova (CCSN), the neutrinos exhibit nonlinear and complex oscillation behaviors due to their self-interactions. The onset of this nonlinear oscillation can be investigated by linearizing the evolution equation for small perturbations around the flavor eigenstates. While the condition under which the flavor eigenstates are unstable has been investigated in many studies, how the perturbations evolve in spacetime has yet to be elucidated. In this paper, we analytically and correctly derive the asymptotic behaviors of the …
A detailed analysis of collective modes that couple to either vector or axial color currents in color-flavor locked phase of color superconducting dense quark matter at finite temperature is presented. Among the realm of collective modes, including the plasmons and the Nambu-Goldstone bosons, we also reveal the gapless Carlson-Goldman modes, resembling the scalar Nambu-Golstone bosons. These latter exist only in a close vicinity of the critical line. Their presence does not eliminate the Meissner effect, proving that the system remains in the color broken phase. The finite temperature properti…
We study the low energy effective action for the collective modes of the color flavor locked phase of QCD. This phase of matter has long been known to be a superfluid because by picking a phase its order parameter breaks the quark-number $U(1)_B$ symmetry spontaneously. We consider the modes describing fluctuations in the magnitude of the condensate, namely the Higgs mode, and in the phase of the condensate, namely the Nambu-Goldstone (or Anderson-Bogoliubov) mode associated with the breaking of $U(1)_B$. By employing as microscopic theory the Nambu-Jona Lasinio model, we reproduce known resul…
The dense neutrino flux streaming from a core-collapse supernova can undergo self-induced flavor conversion caused by neutrino-neutrino refraction. Numerical studies of these nonlinear effects are challenging because representing the neutrino radiation field by discrete energy and angle bins can easily lead to unphysical solutions. In particular, if the number of angle bins N_a is too small, flavor conversion begins too deep and produces completely spurious results. At the same time, N_a=1 (single-angle approximation) can be a good proxy for the N_a -> infinity limit. Based on a linearized sta…
We examine the feasibility of the Bell test (i.e., detecting a violation of the Bell inequality) with the ATLAS detector in Large Hadron Collider (LHC) at CERN through the flavor entanglement between the B mesons. After addressing the possible issues that arise associated with the experiment and how they may be treated based on an analogy with conventional Bell tests, we show in our simulation study that under realistic conditions (expected from the LHC Run 3 operation) the Bell test is feasible under mild assumptions. The definitive factor for this promising result lies primarily in the fact …
Flavor oscillations in elementary particle physics are related to multi-mode entanglement of single-particle states. We show that mode entanglement can be expressed in terms of flavor transition probabilities, and therefore that single-particle entangled states acquire a precise operational characterization in the context of particle mixing. We treat in detail the physically relevant cases of two- and three-flavor neutrino oscillations, including the effective measure of CP violation. We discuss experimental schemes for the transfer of the quantum information encoded in single-neutrino states …
We study the effect of Majorana transition magnetic moments on the flavor evolution of neutrinos and antineutrinos inside the core of Type-II supernova explosions. We find non-trivial collective oscillation effects relating neutrinos and antineutrinos of different flavors, even if one restricts the discussion to Majorana transition electromagnetic moment values that are not much larger than those expected from standard model interactions and nonzero neutrino Majorana masses. This appears to be, to the best of our knowledge, the only potentially observable phenomenon sensitive to such small val…
We study the flavor evolution of a dense gas initially consisting of pure mono-energetic $ν_e$ and $\barν_e$. Using adiabatic invariants and the special symmetry in such a system we are able to calculate the flavor evolution of the neutrino gas for the cases with slowly decreasing neutrino number densities. These calculations give new insights into the results of recent large-scale numerical simulations of neutrino flavor transformation in supernovae. For example, our calculations reveal the existence of what we term the ``collective precession mode''. Our analyses suggest that neutrinos which…
Collective flavor oscillations driven by neutrino-neutrino self interaction inside core-collapse supernovae have now been shown to bring drastic changes in the resultant neutrino fluxes. This would in turn significantly affect the diffuse supernova neutrino background (DSNB), created by all core-collapse supernovae that have exploded in the past. In view of these collective effects, we re-analyze the potential of detecting the DSNB in currently running and planned large-scale detectors meant for detecting both electron neutrinos and antineutrinos. The next generation detectors should be able t…
