AAWSAP DIRD, Quantum Tomography of Negative Energy States in the Vacuum, January 2011

Text

This text came with the file. It may have mistakes. When the text and the image disagree, the image is right.

UNCLASSIFIED//FOR 0551CIAk l::181: 8HLY
Balanced Homodyne System for Casimir Cavities
What has not been experimentally measured yet are the sub-vacuum fluctuations and
their (negative) energy density inside a Casimir cavity.
Marecki (5, 6] theoretically
evaluated the use of BHDs for this purpose. He proposed that a BHD can be used to
detect and spatially map the sub-vacuum fluctuation region inside a Casimir cavity as
well as measure its negative energy density spectrum.
Marecki discovered that by
exploiting a trick with the subtraction of the output of balanced photodiodes, it is
possible to quantify the fluctuations of the quantum field (even in the vacuum!), which
uniquely addresses Davies and Ottewill's [54] negative energy detector hypothesis.
The quantity of interest (to be measured) is the fluctuations of the quantum electric
field \ Ei( l,t) Eil,t)ls (for fields restricted to the frequency w of the local oscillator)
~ r
for squeezed and vacuum states, where E;{ x ,t) is the quantum electric field operator
(in ground-state representation and restricted in frequencies) at the point x, t
~ r
represents the time-dependence of E;(x,t), and ( ... )s stands for the expectation value
with respect to an arbitrary initial state S (vacuum, squeezed, ground state, coherent,
thermal, etc.) of the quantum radiation field under study. (E;(l,t)Ej(l ,t)Js is also
called a two-point function . In quantum field theory, the expectation value (or matrix
element) computed by inserting a product of two quantum operators between two
states, usually the vacuum states, is called a two-point function. This quantity
suggests a "relation" between two states in the same dynamics, and it expresses the
fluctuations of a quantum field. The product of n-operators is called then-point
function which expresses the higher moments of the quantum field fluctuations.
The goal of the experiment is that a state S of the quantum radiation field under study
needs to be characterized by its n-point functions. The typical solution in quantum
optics is to use well-characterized quantum systems interacting in a simple way with
the quantum rad iation field . The detection scheme uses the simple model of a PIN
junction photodiode in which a single electron interacts with the quantum radiation field
under study. This simple interaction means that the state space of the electron can be
severely restricted, the interaction is assumed to be linear in the quantum field, and so
the Born approximation can be used (5, 6]. The PIN junction model of the
photodetection process is an electron in an initial state IO)@S, with its bound-state IO)
l
well-localized around a certain point x0, that gets excited to the continuum of
scattering states I q) by the quantum field state of interest S such that the final states
of the system are liJ)@S .**** The excitation is caused by the linear (dipole
approximation) interaction with the quantum electric field which is
..,, The symbol @ denotes the tensor product of two quantum eigenstates such that Ia1, a2) =Ia1) © Ia2) for
factorized eigenstates which correspond to independent measurements.
UNCLASSIFIED//f8tt 8fflf!IAL Y!IIE 8HLY
36