A representation-free description of the Kasevich-Chu interferometer: a resolution of the redshift controversy

Motivated by a recent claim by Muller et al (2010 Nature 463 926-9) that an atom interferometer can serve as an atom clock to measure the gravitational redshift with an unprecedented accuracy, we provide a representation-free description of the Kasevich-Chu interferometer based on operator algebra. We use this framework to show that the operator product determining the number of atoms at the exit ports of the interferometer is a c-number phase factor whose phase is the sum of only two phases: one is due to the acceleration of the phases of the laser pulses and the other one is due to the acceleration of the atom. This formulation brings out most clearly that this interferometer is an accelerometer or a gravimeter. Moreover, we point out that in different representations of quantum mechanics such as the position or the momentum representation the phase shift appears as though it originates from different physical phenomena. Due to this representation dependence conclusions concerning an enhanced accuracy derived in a specific representation are unfounded.

I. Nickel-Exchanged Zincosilicate Catalysts for the Oligomerization of Propylene and II. Organic SDA-Free Catalysts for the Methanol-to-Olefins Reaction

Nickel-containing catalysts are developed to oligomerize light olefins. Two nickel-containing zincosilicates (Ni-CIT-6 and Ni-Zn-MCM-41) and two nickel-containing aluminosilicates (Ni-HiAl-BEA and Ni-USY) are synthesized as catalysts to oligomerize propylene into C_3n (C₆ and C₉) products. All catalysts oligomerize propylene, with the zincosilicates demonstrating higher average selectivities to C_3n products, likely due to the reduced acidity of the Zn heteroatom.

To test whether light alkanes can be incorporated into this oligomerization reaction, a supported homogeneous catalyst is combined with Ni-containing zincosilicates. The homogeneous catalyst is included to provide dehydrogenation/hydrogenation functions. When this tandem catalyst system is evaluated using a propylene/n-butane feed, no significant integration of alkanes are observed.

Ni-containing zincosilicates are reacted with 1-butene and an equimolar propylene/1-butene mixture to study other olefinic feeds. Further, other divalent metal cations such as Mn²⁺, Co²⁺, Cu²⁺, and Zn²⁺ are exchanged onto CIT-6 samples to investigate stability and potential use for other reactions. Co-CIT-6 oligomerizes propylene, albeit less effectively than Ni-CIT-6. The other M-CIT-6 samples, while not able to oligomerize light olefins, may be useful for other reactions, such as deNO_x.

Molecular sieves are synthesized, characterized, and used to catalyze the methanol-to-olefins (MTO) reaction. The Al concentration in SSZ-13 samples is varied to investigate the effect of Al number on MTO reactivity when compared to a SAPO-34 sample with only isolated Si Brønsted acid sites. These SSZ-13 samples display reduced transient selectivity behavior and extended reaction lifetimes as Si/Al increases; attributable to fewer paired Al sites. MTO reactivity for the higher Si/Al SSZ-13s resembles the SAPO-34 sample, suggesting that both catalysts owe their stable reaction behavior to isolated Brønsted acid sites.

Zeolites CHA and RHO are prepared without the use of organic structure-directing agents (OSDAs), dealuminated by steam treatments (500°C-800°C), and evaluated as catalysts for the MTO reaction. The effects of temperature and steam partial pressure during steaming are investigated. X-ray diffraction (XRD) and Ar physisorption show that steaming causes partial structural collapse of the zeolite, with degradation increasing with steaming temperature. ²⁷Al MAS NMR spectra of steamed materials reveal the presence of tetrahedral, pentacoordinate, and hexacoordinate aluminum.

Proton forms of as-synthesized CHA (Si/Al=2.4) and RHO (Si/Al=2.8) rapidly deactivate under MTO testing conditions (400°C, atmospheric pressure). CHA samples steamed at 600°C performed best among samples tested, showing increased olefin selectivities and catalyst lifetime. Acid washing these steamed samples further improved activity. Reaction results for RHO were similar to CHA, with the RHO sample steamed at 800°C producing the highest light olefin selectivities. Catalyst lifetime and C₂-C₃ olefin selectivities increase with increasing reaction temperature for both CHA-type and RHO-type steamed samples.