Neutron Interferometry Research Articles

Precision measurement of the coherent neutron scattering length of 3He through neutron interferometry

Improved knowledge of the real part of the neutron scattering length of 3He is important for further development of nuclear few-body theory, as well as for a thorough understanding of neutron scattering off quantum liquids. The real part of the bound incoherent neutron scattering length bi' has recently been measured directly with an experimental uncertainty of better than 1% by means of spin echo spectrometry. The uncertainty of the more fundamental bound multiplet scattering lengths b±' is thus limited by today's 1.2% uncertainty of the spin-independent coherent part bc'. Employing the skew-symmetric perfect crystal Si-interferometer at the S18 experimental site at ILL, Grenoble, we have re-measured the real part of the bound coherent neutron scattering length bc' of 3He. Our result bc' = 6.010(21)fm exhibits a significant deviation compared to the latest accepted value bc' = 5.74(7)fm (H. Kaiser, H. Rauch, G. Badurek, W. Bauspiess, U. Bonse, Z. Phys. A 291, 231 (1979)). Including the known value of the incoherent neutron scattering length, we obtain new values for the real parts of the free singlet and triplet scattering lengths, a-' = 7.573(30)fm and a+' = 3.480(18)fm. Our result contravenes by more than 7 standard deviations the measurement of the same physical quantity that has recently been performed by a group at NIST in a very similar experiment (P.R. Huffman, D.L. Jacobson, K. Schoen, M. Arif, T.C. Black, W.M. Snow, S.A. Werner, Phys. Rev. C 70, 014004 (2004)) which yielded bc' = 5.853(7)fm.

Topological phase for entangled two-qubit states and the representation of theSO(3) group

We discuss the representation of the $SO(3)$ group by two-qubit maximally entangled states (MES). We analyze the correspondence between $SO(3)$ and the set of two-qubit MES which are experimentally realizable. As a result, we offer a new interpretation of some recently proposed experiments based on MES. Employing the tools of quantum optics we treat in terms of two-qubit MES some classical experiments in neutron interferometry, which showed the $\pi $-phase accrued by a spin-$1/2$ particle precessing in a magnetic field. By so doing, we can analyze the extent to which the recently proposed experiments - and future ones of the same sort - would involve essentially new physical aspects as compared with those performed in the past. We argue that the proposed experiments do extend the possibilities for displaying the double connectedness of $SO(3)$, although for that to be the case it results necessary to map elements of $SU(2)$ onto physical operations acting on two-level systems.

The fundamental neutron physics facilities at NIST

The National Institute of Standards and Technology (NIST) Center for Neutron Research (NCNR) is a national center that provides thermal and cold neutrons beams for activities such as condensed matter physics, materials science, nuclear chemistry, and biological science. Four beams are currently in use for fundamental physics experiments. These include a high-intensity polychromatic beam, a 0.496nm monochromatic beam, a 0.89nm monochromatic beam, and a neutron interferometer and optics facility. Experiments focus primarily on studies of the weak interaction using neutrons. This paper provides a general overview of the facilities and highlights some current experiments.

Noncyclic geometric phase due to spatial evolution in a neutron interferometer

We present a split-beam neutron interferometric experiment to test the noncyclic geometric phase tied to the spatial evolution of the system: The subjacent two-dimensional Hilbert space is spanned by the two possible paths in the interferometer, and the evolution of the state is controlled by phase shifters and absorbers. A related experiment was reported previously by Hasegawa et al. [Phys Rev A 53, 2486 (1996)] to verify the cyclic spatial geometric phase. The interpretation of this experiment, namely to ascribe a geometric phase to this particular state evolution, has met with severe criticism from Wagh [Phys. Rev A 59, 1715 (1999)]. The extension to a noncyclic evolution manifests the correctness of the interpretation of the previous experiment by means of an explicit calculation of the noncyclic geometric phase in terms of paths on the Bloch-sphere.

Space–time torsion contribution to quantum interference phases

The field of neutron interferometry achieved one of its most significant successes with the detection of the influence of gravity in the quantum mechanical phase of a thermal neutron beam. From the latest experimental readouts in this context an intriguing discrepancy has been elicited. Indeed, theory and experiment dissent by one per cent, and though this fact could be a consequence of the mounting of the experimental device, it might also embody a difference between the way in which gravity behaves in classical and quantum mechanics. In this work the effects, upon the interference pattern, of space–time torsion will be analyzed heeding its coupling with the spin of the neutron beam. It will be proved that, even with this contribution, there is enough leeway for a further discussion of the validity of the equivalence principle in nonrelativistic quantum mechanics.

Spatial Non-Cyclic Geometric Phase in Neutron Interferometry.

We present a split-beam neutron interferometric experiment to test the non-cyclic geometric phase tied to the spatial evolution of the system: the subjacent two-dimensional Hilbert space is spanned by the two possible paths in the interferometer and the evolution of the state is controlled by phase shifters and absorbers. A related experiment was reported previously by some of the authors to verify the cyclic spatial geometric phase. The interpretation of this experiment, namely to ascribe a geometric phase to this particular state evolution, has met severe criticism. The extension to non-cyclic evolution manifests the correctness of the interpretation of the previous experiment by means of an explicit calculation of the non-cyclic geometric phase in terms of paths on the Bloch-sphere. The theoretical treatment comprises the cyclic geometric phase as a special case, which is confirmed by experiment.

The Fundamental Neutron Physics Facilities at NIST.

The program in fundamental neutron physics at the National Institute of Standards and Technology (NIST) began nearly two decades ago. The Neutron Interactions and Dosimetry Group currently maintains four neutron beam lines dedicated to studies of fundamental neutron interactions. The neutrons are provided by the NIST Center for Neutron Research, a national user facility for studies that include condensed matter physics, materials science, nuclear chemistry, and biological science. The beam lines for fundamental physics experiments include a high-intensity polychromatic beam, a 0.496 nm monochromatic beam, a 0.89 nm monochromatic beam, and a neutron interferometer and optics facility. This paper discusses some of the parameters of the beam lines along with brief presentations of some of the experiments performed at the facilities.

Virtual Excitation and Multiple Scattering Correction Terms to the Neutron Index of Refraction for Hydrogen.

The neutron index of refraction is generally derived theoretically in the Fermi approximation. However, the Fermi approximation neglects the effects of the binding of the nuclei of a material as well as multiple scattering. Calculations by Nowak introduced correction terms to the neutron index of refraction that are quadratic in the scattering length and of order 10(-3) fm for hydrogen and deuterium. These correction terms produce a small shift in the final value for the coherent scattering length of H2 in a recent neutron interferometry experiment.

Measurement of the Coherent Neutron Scattering Length of (3) He.

By means of neutron interferometry the s-wave neutron scattering length of the (3)He nucleus was re-measured at the Institut Laue-Langevin (ILL). Using a skew symmetrical perfect crystal Si-interferometer and a linear twin chamber cell, false phase shifts due to sample misalignment were reduced to a negligible level. Simulation calculations suggest an asymmetrically alternating measuring sequence in order to compensate for systematic errors caused by thermal phase drifts. There is evidence in the experiment's data that this procedure is indeed effective. The neutron refractive index in terms of Sears' exact expression for the scattering amplitude has been analyzed in order to evaluate the measured phase shifts. The result of our measurement, b' c = (6.000 ± 0.009) fm, shows a deviation towards a greater value compared to the presently accepted value of b' c = (5.74 ± 0.07) fm, confirming the observation of the partner experiment at NIST. On the other hand, the results of both precision measurements at NIST and ILL exhibit a serious 12σ (12 standard uncertainties) deviation, the reason for which is not clear yet.

Towards manageable magnetic field retrieval in bulk materials

We present an extension to a recently introduced method for the tomographic investigation of magnetic domain structures in ferromagnetic solids which is based on a combination of neutron interferometry and neutron depolarization concepts. Methodical development of the reconstruction algorithm yields significant improvement compared to previous versions. This is expressed by fast convergence and by doubling the maximum computable pixel size from 1.7 μ m before to at least 4 μ m , which is an important step towards actual experimental realization of this novel tomographic method. Furthermore, it is demonstrated that our algorithm converges even when, as in a real experiment, the measured values of the observables are subject to statistical fluctuations.

Non-Locality and Contextuality in Neutron Quantum Optics

Entangelement of two photons, or atoms is a complementary situation to a double slit situation of a single photon, neutron or atom. With neutrons single particle interference phenomena can be observed and the “entanglement of degrees of freedom”, i.e. contextuality can be verified. In this respect, neutrons are proper tools for testing quantum mechanics because they are massive, they couple to electromagnetic fields due to their magnetic moment and they are subject to all basic interactions, and they are sensitive to topological effects, as well. Related experiments will be discussed. Deterministic and stochastic partial absorption experiments can be described by Bell-type inequalities. Recent neutron interferometry experiments based on post-selection methods renewed the discussion about quantum non-locality and the quantum measuring process. It has been shown that interference phenomena can be revived even when the overall interference pattern has lost its contrast. This indicates a persisting coupling in phase space even in cases of spatially separated Schrodinger-cat-like situations. These states are extremely fragile and sensitive against any kind of fluctuations and other decoherence processes. More complete quantum experiments also show that a complete retrieval of quantum states behind an interaction volume becomes impossible in principle.

Interfering with the neutron spin

Charge neutrality, a spin 1/2 and an associated magnetic moment of the neutron make it an ideal probe of quantal spinor evolutions. Polarized neutron interferometry in magnetic field Hamiltonians has thus scored several firsts such as direct verification of Pauli anticommutation, experimental separation of geometric and dynamical phases and observation of non-cyclic amplitudes and phases. This paper provides a flavour of the physics learnt from such experiments.

New intensity and visibility aspects of a double-loop neutron interferometer

Various phase shifters and absorbers can be put into the arms of a double loop neutron interferometer. The mean intensity levels of the forward and diffracted beams behind an empty four plate interferometer of this type have been calculated. It is shown that the intensities in the forward and diffracted direction can be made equal using certain absorbers. In this case the interferometer can be regarded as a 50/50 beam splitter. Furthermore the visibilities of single and double loop interferometers are compared to each other by varying the transmission in the first loop using different absorbers. It can be shown that the visibility becomes exactly 1 using a phase shifter in the second loop. In this case the phase shifter in the second loop must be strongly correlated to the transmission coefficient of the absorber in the first loop. Using such a device homodyne-like measurements of very weak signals should become possible.

An epoch in cold neutron interferometry for fundamental physics—development of multilayer interferometer

The development of cold neutron interferometry using multilayer mirrors is reviewed. Our new devices based on etalon plates have made a breakthrough for large-scale multilayer interferometers. In order to obtain much larger area enclosed by the two paths of interferometer, we are developing a Mach–Zehnder type interferometer. To fulfill the severe requirement for aligning the four mirrors, we utilize six solid-etalon-plates coated with multilayer mirrors and a high precision flat base plate.

Quantum-engineered neutron states and phase space manipulations

In neutron interferometry and in spin-echo systems non-classical neutron quantum states can be produced and manipulated. Schrödinger cat-like states exhibit two spatially separated regions which are occupied by the neutron at the same time. When used in scattering experiments this enables a direct observation of the local structure and dynamics of matter. A proper description can be obtained by means of Wigner quasi-distribution functions which are common in quantum optics. More complicated quasi-distribution functions have been verified recently by means of a double loop interferometer. These quantum states have the capacity to observe even higher-order correlation functions characterizing condensed matter. The non-local character of quantum theory has also been demonstrated in the behavior of neutrons within narrow slits where typical confinement effects have been observed. Such Casimir-like and Zeno-like phenomena show how neutrons are an attractive tool for quantum optical experiments opening new possibilities of neutron phase space manipulations. A proper treatment of the neutron field can enhance the available neutron intensities considerably. First cooling to ultra-cold neutron energies by cold solid deuterium moderators increases the phase space density, which can be transferred to higher energies by a proper phase space transformer consisting of fast rotating multi-layer mirrors or crystals. Various proposals in this directions will be discussed.

Spin dynamics in polarized neutron interferometry

An appropriate formalism is developed which describes the effect of simultaneous occurrence of nuclear and magnetic interaction caused by an arbitrary structure of sequential magnetic domains on the emerging intensity and polarization.

Quantum-engineered neutron states and phase space manipulations

In neutron interferometry and in spin-echo systems non-classical neutron quantum states can be produced and manipulated. Schrödinger cat-like states exhibit two spatially separated regions which are occupied by the neutron at the same time. When used in scattering experiments this enables a direct observation of the local structure and dynamics of matter. A proper description can be obtained by means of Wigner quasi-distribution functions which are common in quantum optics. More complicated quasi-distribution functions have been verified recently by means of a double loop interferometer. These quantum states have the capacity to observe even higher-order correlation functions characterizing condensed matter. The non-local character of quantum theory has also been demonstrated in the behavior of neutrons within narrow slits where typical confinement effects have been observed. Such Casimir-like and Zeno-like phenomena show how neutrons are an attractive tool for quantum optical experiments opening new possibilities of neutron phase space manipulations. A proper treatment of the neutron field can enhance the available neutron intensities considerably. First cooling to ultra-cold neutron energies by cold solid deuterium moderators increases the phase space density, which can be transferred to higher energies by a proper phase space transformer consisting of fast rotating multi-layer mirrors or crystals. Various proposals in this directions will be discussed.

Violation of a bell-like inequality in single-neutron interferometer experiments: Quantum contextuality

A neutron interferometer experiment which clearly demonstrates the violation of a Bell-like inequality is reported. Entanglement is achieved not between particles, but between the degrees of freedom, in this case, for a single particle. The total wave function of spin-1/2 neutron is described in a tensor product Hilbert space. Appropriate combinations of the direction of spin analysis and the position of the phase shifter allow experimental verification of the violation of a Bell-like inequality. Manipulation of the wave function in one Hilbert space influences the result of the measurement in the other Hilbert space: manipulation without touch! The violation of the Bell-like inequality is discussed in terms of quantum contextuality and an entanglement-induced correlation.

Berry and Pancharatnam topological phases of atomic and optical systems

Theoretical and experimental studies of Berry and Pancharatnam phases are reviewed. Basic elements of differential geometry are presented for understanding the topological nature of these phases. The basic theory analyzed by Berry in relation to magnetic monopoles is presented. The theory is generalized to nonadiabatic processes and to noncyclic Pancharatnam phases. Different systems are discussed including polarization optics, n-level atomic systems, neutron interferometry and molecular topological phases.

Berry phase in entangled systems: A proposed experiment with single neutrons

The influence of the geometric phase, in particular the Berry phase, on an entangled spin-(1/2) system is studied. We discuss in detail the case, where the geometric phase is generated only by one part of the Hilbert space. We are able to cancel the effects of the dynamical phase by using the 'spin-echo' method. We analyze how the Berry phase affects the Bell angles and the maximal violation of a Bell inequality. Furthermore we suggest an experimental realization of our setup within neutron interferometry.