It is well established that in physics all systems including the electromagnetic field, have to be treated as quantum systems. In general, repeated measuremnet of one of the observable quantitiesleads to an average value around which there are quantum fluctuations or noise. The quantum noise is a fundamental property of all systems,and persists even if all classical sources of error have been eliminated from the measurement process. Quantum fluctuations are present in all systems, including radiation fields in the vacuum state, and it has long been thought that they presented an insuperable barrier to accuracy. They limit the sensitivity achieved by detectors for spectral resolution and the signal-to-noise ratio and hence limit accuracy of any measurement. All detection systems are subject to this limit, and it was long believed that this limit could not be suppressed. In 1980's theoretical studies followed by experimental measurements have shown that the quantum limit could be circumvented. The search for light fields and physical systems with reduced or evencompletely suppressed fluctuations has become a new subject for physics to study. The possiblity to overcome the quantum limit with new sourcesof light allows researches to perform experiments with greater precision than possible with laser light.
The general field of quantum-limit spectroscopy is of importance in connection with the physical theories of noise-free measurements. The field of study of spectroscopic effects at the quantum noise limit is either explicit or implicit in almost all areas of physics and also in many areas of science such as chemistry and biology, and we intend to explore novel effects and recent developments in spectroscopy of molecules. Quantum effects in atomic radiation, which are distinct from semiclassical theories, arise when it is essential to quantize the electromagnetic field, and it is well known that they were central to early discussions of the manifestation of the vacuum fluctuations characteristic of quantum fields. In the field of quantum optics one could perhaps take the interest in quantum spectroscopic effects to date from the work on the fluorescence and absorption spectra by Mollow, photon antibunching and squeezing by Kimble, Mandel, Walls, Carmichael and other workers in the seventies. In recent years quantum spectroscopy has become of interest not only for the basic understanding of complicated quantum structure of atomic systems, but also because it lies at the heart of such important applications as the high resolution spectroscopy and atomic clocks. The latest applications are to quantum computation and to spectroscopy with Bose-Einstein condensates. It has also been demonstrated that quantum and precision spectroscopy methods provide an effective way of controlling quantum fluctuations and decoherence. Other rapidly developing modern topics, such as entanglement, enhanced spectral resolution and controlled information transfers, are of course intimately associated with quantum effects in the atom-field interaction.
Although this book is focused on a small collection of current research areas in atomic spectroscopy, it should nevertheless be evident how strongly atomic spectroscopy relates to basic quantum physics and quantum limits in particular. Quantum-limit spectroscopy lies at the frontier of current experimental and theoretical techniques, and is one of the areas of atomic spectroscopy where the quantization of the sources (atoms) and the field is essential to predict and interpret the existing experimental results. It was recognized as representing a radical departure from the traditional classical spectroscopy where the existing treatments turn out to be less than completely satisfactory. Currently, there is an increasing interest in quantum and precision spectroscopy both theoretically and experimentally, due to a significant progress in trapping and cooling of single atoms and ions. This progress allows to explore in the most intimate detail the ways in which light interacts with atoms and to measure spectral properties and quantum effects with a large precision. Moreover, it allows to perform subtle tests ofquantum mechanics on the single atom and single photon scale which were hardly even imaginable as "thought experiments'' a few years ago.
Some description of the mathematical tools for the study of quantum spectroscopy is required, and therefore we begin in Chap. 1 with an overview of the fundamental concepts relating to quantum fluctuations of the electromagnetic field and the spectroscopic methods of detecting them by means of photoelectron counting. Further, the intensity spectrum, optical spectrum, and quantum noise spectrum will be defined. In Chap. 2, we begin the analysis of quantum-limit spectroscopy with a consideration of the most fundamental models in atomic spectroscopy. In particular, we consider the optical spectra of a two-level atom driven by a different types of fields.
Back to the top1. Optical Spectra and Their Measurements
1.1 Definition of the physical spectrum
1.2 Excitation spectrum of an atomic system
1.3 Emission (fluorescence) spectrum of radiated field
1.4 Coherent (elastic) component
1.5 Incoherent (noise) component
1.6 Absorption spectra of a probe field
1.7 Phase-dependent spectra and their measurements
1.8 Spectral analyzers
1.9 Laser modulation techniques for spectroscopic studies
2. Spectroscopy with Single Atoms in Atomic Beams
2.1 Fluorescence spectra with a monochromatic driving field
2.1.1. Transient spectra
2.1.2. Stationary spectra
2.1.3. Photodetector bandwidth effects
2.2 Fluorescence spectra with a multichromatic driving field
2.2.1. Frequency-modulated excitation
2.2.2. Amplitude-modulated excitation
2.2.3. Polychromatic excitation
2.3. Phase control of optical spectra
2.4. Driving the atom by a superposition of coherent states
2.5. Spectroscopy with atoms with permanent dipole moments
2.6. Transitions at the Rabi frequencies
2.7. Driving an atom by classical and quantum fields
2.8. Narrowing of the spectral lines via coherent pumping
2.9. Experimental observation of the spectral line narrowing
3. Collective Multiatom Spectroscopy
3.1 Superradiant and subradiant emission\\
3.2 Signatures of the collective interaction in optical spectra
3.3 Weak-field limit
3.4. Strong-field limit
3.5. Quantum effects in multiatom spectroscopy
3.5.1. Photon antibunching and superbunching
3.5.2. Squeezing and spin squeezing
3.5.3. Multiatom entanglement
3.6. Signatures of multiatom entanglement in optical spectra
3.7 High-field approximations in multi-atom spectroscopy
3.8. Multiatom entangled states and decoherence
3.9. Quantum information processing in atomic systems
3.9.1. Population transfer between coupled atoms
3.9.2. Population transfer between distant atoms
3.10. Quantum logic gates in atomic systems
4. Excitation and Probe Spectroscopy
4.1. Emission line shapes
4.2. Probe absorption profiles
4.3 Amplification without population inversion
4.4. Lasing without inversion
4.5. Probe of light fluctuations and population trapping
4.6. Detection of atomic internal states and state control
4.7. Quantum state measurement from the absorption spectrum
5. Time-Dependent Fluorescence Spectroscopy
5.1. Coherent excitation of atoms by a pulse trains
5.2. Coherent transients in the fluorescence spectrum
5.3. Time-dependent fluorescence and absorption spectra
5.3.1. Atoms prepared in bare states
5.3.2. Atoms prepared in pure dressed states
6. Nonclassical Effects in Optical Spectra
6.1. Criteria for nonclassicality
6.2. Narrowing of the spectral lines
6.3. Spectral hole burning
6.4. Anomalous features
6.5. Phase dependent fluorescence and absorption spectra
6.6. Driving the atom by atomic fluorescence
6.7. Electron shelving and quantum jumps
6.8. Experimental observations of quantum jumps
7. Spectroscopy with Atoms in Frequency-Dependent Reservoirs
7.1. Quantum-reservoir engineering
7.2. Selective excitation via quantum-reservoir engineering
7.3. One-dimensional atom
7.4. Dynamically suppressed and induced fluorescence
7.5. Spectroscopy with atoms in optical cavities
7.5.1. Theoretical analysis of spectral properties of emitted and transmitted fields
7.5.2. Nonclassical effects in emitted and transmitted fields
7.6. Experimental studies of spectral effects in optical cavities
7.7. Experimental studies of nonclassical effects in optical cavities
8. Quantum Spectroscopy with Squeezed Light
8.1. Generation of squeezed light
8.2. Application of squeezed light in atomic spectroscopy
8.2.1. Excitation with broadband squeezed light
8.2.2. Excitation with narrowband squeezed light
8.3. Signatures of squeezing in optical spectra
8.3.1. Spectral line narrowing
8.3.2. Amplification without population inversion
8.3.3. Population trapping
8.4. Application of squeezed light to entanglement creation
8.5. Frequency metrology with squeezed light
8.6. Spectrum of squeezing
8.7. Experimental observation of squeezing in the phase-dependent spectrum
8.8. Quantum spectroscopy with squashed light
8.9. Spin squeezed states
8.10. Applications of spin squeezing in spectroscopy and measurement theory
8.11. Experimental observations of squeezing induced quantum effects
9. Spectroscopy with Trapped Atoms and Ions
9.1. Detection of single atoms and ions\\
9.2. Trapped atoms interacting with optical fields
9.3. Laser cooling of trapped atoms and ions
9.3.1. Cooling in running waves
9.3.2. Cooling in a standing-wave
9.4. Quantum dynamics of single trapped ions
9.5. Fluorescence spectrum of trapped single atoms
9.5.1. Theoretical description
9.5.2. Experimental observation
9.6. Motional effects in the fluorescence spectrum
9.7. Nonclassical states of motion in ion traps
9.8. Nonclassical effects in resonance fluorescence of trapped ions
9.9. Experiments with one and two trapped ions
10. Precision Optical Spectroscopy
10.1. Quantum-mechanical limits in optical spectroscopy
10.1.1. Heisenberg limit
10.1.2. Diffraction limit
10.2. Beyond the quantum limits
10.3. Signal-to-noise ratio with a quantum field
10.4. Spectral resolution with a quantum field
10.5. Entanglement enhanced spectral resolution
10.5.1. Resolution with two-photon entangled states
10.5.2. Resolution with multi-photon entangled states
10.6. Experimental demonstration of entangled multi-photon resolution
10.7. Optical frequency standard and cold atom clocks
10.8. Stabilization and measurement of optical frequencies
10.9. Quantum optical lithography
10.10. Quantum metrology
11. Polarization Spectroscopy
11.1. Selective polarization dependent excitation of atomic transitions
11.2. Generation of polarization entangled states
11.3. Sources of polarization-entangled photons
11.4. Applications to laser frequency locking
11.5. Quantum image control
12. Spectroscopic Measurements of Quantum Fluctuations of Light
12.1 Light sources and their fluctuations
12.2. Homodyne detection of the fluorescence field
12.3. Spectral filtering of light
12.4. Spectrum of the second-order correlations
12.5. Storage of photons in dressed atomic states
13. Spectroscopic Measurements of Decoherence
13.1. Sources of decoherence
13.2. Signatures of decoherence in optical spectra
13.3. Dynamical suppression of decoherence
13.4. Suppression of decoherence via collective interaction
13.5. Control of decoherence by frequency modulation
13.6. Coherent control of a quantum system
13.7. Decoherence in the motion of single atoms
14. Quantum Spectroscopy with Frequency-Entangled Photon Pairs
14.1. Generation of frequency-entangled photon pairs
14.2. Spectroscopy with frequency-entangled photon pairs
14.3. Experiments with frequency-entangled photons