Transcript Highligh in Physics 2005
Congresso del Dipartimento di Fisica Highlights in Physics 2005
11–14 October 2005, Dipartimento di Fisica, Università di Milano
Generation and decoherence of mesoscopic superposition states in a strongly driven micromaser
F. Casagrande and A. Lulli Dipartimento di Fisica, Università di Milano CNR-INFM – Sezione di Milano
INFM
ABSTRACT
Decoherence, that is the loss of coherence between the states of a quantum system induced by the environment, is an intriguing subject both for basic investigations on the elusive boundary between the quantum and the classical worlds, and for applications in quantum information and computation. We show [1] that the decoherence of mesoscopic superposition states of a cavity field can be observed in a micromaser where a classical field strongly drives the atoms, that is, in a solvable and experimentally feasible system [2]. We provide an analytical description in phase space of all stages of atom-pair correlation measurements at steady-state, where the detection of the first probe atom prepares a superposition field state, that entangles with the second probe atom. The conditional probabilities for the detection of the latter atom provide a description of the decoherence of the superposition state, which occurs in an open system in the presence of pumping, driving, dissipative, and thermal effects. The decoherence rate is proportional to the squared interaction time, that rules the separation in phase space between the superposition components, whereas the quantum coherence is unaffected by the atomic pumping. Hence we further investigate the system when the cavity is not pumped. Starting the correlation measurements from the vacuum state, the superposition states are maximally separated Schr ödinger cat states, whose decoherence can be thus monitored.
A SIMPLE INTRODUCTION
One of the most intriguing problems in modern physics is to explain the emergence of the classical appearance of the macroscopic world from the quantum mechanical laws that rule the behavior of matter at the microscopic level.
The fundamental features of quantum mechanics, such as linearity and entanglement, imply the occurrence of interference effects and nonlocal correlations, giving rise to seemingly paradoxical behaviors that we do not see in the world around us. As early as in 1933 Schrödinger pointed out these problems by a caricatural metaphor, in which he described a cat in a closed box containing a diabolic apparatus correlating his life or death to the excited or unexcited state of an atom. It is then impossible to know if the cat is alive or dead, until the box is opened and only one of the two possibilities is observed.
The absence of superposition states and hence interference effects in the macroscopic domain originates from the fact that no macroscopic system is isolated; the unavoidable interaction with the environment induces a decay of quantum coherence, or the way to the observation of decoherence
in progress
decoherence
, that is so fast to be practically instantaneous. However, the generation and control of systems of
mesoscopic
size opened . This was done by Haroche and coworkers [3], working in cavity quantum electrodynamics, where systems of atoms and photons can be controlled with exquisite accuracy. In the experiment they generated superpositions of two coherent cavity field states with the same amplitude but different phases, and were able to monitor their decoherence for the first time. States of this kind, though not macroscopic, are usually called
Schrödinger cats
after the famous paradox.
Besides its deep fundamental importance, the study of decoherence plays a central role in quantum information and communication. Here just the most peculiar features of quantum mechanics allow implementing classically impossible processes, and just decoherence is the main obstacle to the implementation of logic gates and other basic operations in quantum computation.
STRONGLY DRIVEN MICROMASER AND ATOMIC CORRELATIONS
We investigated the Strongly Driven Micromaser [2], in which a beam of two-level atoms crosses a superconductive microwave cavity where the atomic transition is resonant with one cavity mode.
Like in the micromaser, atoms cross the cavity one at a time. Furthermore, during the passage the atoms are strongly driven by classical field.
SCHEMATIC SYSTEM SET-UP GENERATION AND DECOHERENCE OF MESOSCOPIC SUPERPOSITION STATES
We studied [1] the dynamics of the cavity field states prepared by the detection of outgoing atoms in the upper or lower state. We described in phase space all stages of atom pair correlation measurements (see below), in which the detection of the first atom generates a mesoscopic superposition state of the cavity field, that later entangles with a second atom. The decoherence of the superposition is described by conditional atomic probabilities. It depends on the squared interaction time, that is the parameter ruling the separation in phase space between the components of the states, whereas it is independent of the atomic pumping rate.
DECOHERENCE OF SCHR ÖDINGER CAT STATES
We considered the case that the atomic correlation measurements occur in the absence of atomic pumping, starting from the cavity in a thermal state. This allowed us to isolate and describe the effects of temperature on decoherence.
We further investigated the system in the limit of negligible temperature, in which the correlation measurements start from the vacuum state of the cavity field. In this case the system dynamics depends only on the dimensionless interaction time and can be solved even without phase space techniques. Furthermore, the mesoscopic superpositions are exactly
Schr ödinger cats
(see below). Hence the decoherence of cat states can be monitored by an alternative method that can offer same advantages over the one in the Haroche experiment [3].
Atomic beam oven QUANTUM CHARACTERISTIC FUNCTION OF THE STEADY-STATE CAVITY FIELD QUANTUM CHARACTERISTIC FUNCTION OF A CAT STATE Laser excitation
e
Microwave Cavity Field ionization
g
External driving field
4
ATOM PAIR CORRELATION FUNCTIONS
The dynamics of this quantum open system was analytically solved in spite of the presence of driving, pumping, and dissipative effects. One of the main results is the prediction of remarkable atomic correlations when the system operates at steady state, showing bunching and anti bunching effects depending on the atomic states (see below). Another relevant feature is that these correlations decays much faster than the dissipative decay of the cavity field.
1 2 0 .
05 0 .
05 4 1 2
e g
1 2
e g
Parameters:
| |
Dimensionless interaction time
Dimensionless correlation time
Parameters:
Atomic pumping rate
N ex
10
Dimensionless interaction time
Mean thermal photon number
n
0 .
03
DECOHERENCE SIGNAL
P
P
e
/
g
cosh 8 cosh 1 2 8 1 2 2
e
2 2 1 1
DECOHERENCE RATE Dissipative rate
D
2 2 2
gt
int 2
Coupling frequency Interaction time NEXT INVESTIGATIONS
We shall investigate the
entanglement
of both the driven atom-cavity field system, at the basis of the decoherence studies, and the atom atom system, to elucidate the nature of atomic correlations.
Dissipative decay REFERENCES [1] F. Casagrande and A. Lulli, Eur. Phys. J. D 36, 123 (2005); J. Opt. B: Quantum Semiclass. Opt. (2005), in press.
[2] F. Casagrande et al, Phys. Rev. A 69, 023812 (2004); Opt. Spectrosc. 99, 301 (2005).
[3] M. Brune et al., Phys. Rev. Lett. 77, 4887 (1996).