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Laser Physics Letters

Photon-induced correlations of quantum systems via an excitation exchange operator

R. Shuker, Gennady A. Koganov

Published Apr 20, 2021• 4 citations
Publisher

Abstract

Abstract The sensitivities of optical magnetometers, atomic clocks and atom interferometers and other quantum metrology devices, whose signals are linear in the number N of active atoms, have practically arrived at their theoretical limit. Further enhancement of the sensitivities of such devices requires the introduction of new physical processes to improve on their present achievements. Many-body collective correlation among the atoms, spins or, in general, quantum systems may prove to be a suitable method. As such correlations introduce interference terms in the intensity of the scattering amplitudes they may enhance the signal as N ( N − 1) for N correlated quantum systems. These correlations enhance the signal to noise ratio by a factor of N 2 and contribute to better sensitivity in quantum metrology. Moreover, atomic correlation may provide a quantum noise limit, the Heisenberg limit. In the present letter a novel operator is introduced that expresses photon-induced excitation exchange that takes into account energy conservation, V i j = a ˆ † σ i σ j † a ˆ , where σ i = g i e i is the lowering operator of the i - th atom, and a ˆ † , a ˆ are photon creation and annihilation operators. Here i and j stand for two different atoms. This operator describes real or virtual photon-assisted excitation exchange between two atoms. Moreover, it conserves the total number of excitations in the joint electromagnetic field and the quantum system. A photon-induced excitation exchange between two atoms is calculated and clearly exhibits correlation and collective effects.

DOI
10.1088/1612-202x/abf242

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Abstract The sensitivities of optical magnetometers, atomic clocks and atom interferometers and other quantum metrology devices, whose signals are linear in the number N of active atoms, have practically arrived at their theoretical limit. Further enhancement of the sensitivities of such devices requires the introduction of new physical processes to improve on their present achievements. Many-body collective correlation among the atoms, spins or, in general, quantum systems may prove to be a suitable method. As such correlations introduce interference terms in the intensity of the scattering amplitudes they may enhance the signal as N ( N − 1) for N correlated quantum systems. These correlations enhance the signal to noise ratio by a factor of N 2 and contribute to better sensitivity in quantum metrology. Moreover, atomic correlation may provide a quantum noise limit, the Heisenberg limit. In the present letter a novel operator is introduced that expresses photon-induced excitation exchange that takes into account energy conservation, V i j = a ˆ † σ i σ j † a ˆ , where σ i = g i e i is the lowering operator of the i - th atom, and a ˆ † , a ˆ are photon creation and annihilation operators. Here i and j stand for two different atoms. This operator describes real or virtual photon-assisted excitation exchange between two atoms. Moreover, it conserves the total number of excitations in the joint electromagnetic field and the quantum system. A photon-induced excitation exchange between two atoms is calculated and clearly exhibits correlation and collective effects.
Collective Photon Assisted Dressing of Atomic Levels by the number NNN of Correlated Atoms
Enhancement of the sensitivities of optical magnetometers, atomic clocks and atom interferometers and other quantum metrology devices requires introducing new physical processes to improve on their present achievements. Many body collective correlations among the atoms, spins or, in general, quantum systems may prove to be a suitable method. As these correlations introduce interference terms in the intensity of the scattering amplitudes, they may enhance the signal as N(N−1)N(N-1)N(N−1) for N correlated quantum systems. These correlations enhance the signal to noise ratio by a factor of N2N^2N2 and contribute to better sensitivity in quantum metrology. Moreover atomic correlation may provide quantum noise limit, Heisenberg limit. In the present communication excitation exchange induced by photons in a cavity between two atoms is calculated and clearly exhibits correlation and collective effects. A novel operator is introduced that expresses photon-induced excitation exchange that takes in account energy conservation, Vij=a^†σiσj†a^V_{ij}=\hat{a}^\dagσ_iσ_j^†\hat{a}Vij​=a^†σi​σj†​a^, σi=∣g⟩i⟨e∣iσ_i=\left|g\right\rangle_{i}\left\langle e\right|_{i}σi​=∣g⟩i​⟨e∣i​ is lowering operator of iii-th atom, and a^†,a^\hat{a}^†,\hat{a}a^†,a^ are photon creation and annihilation operators. Here iii and jjj stand for two atoms. This operator describes real or virtual photon assisted dipole-dipole interaction. Moreover, it conserves the total number of excitations in the joint em field and the quantum system. Experimental challenges are suggested.
We study the quantum statistical properties of the collective excitations of an atomic ensemble inside a high-finesse cavity. In the large-detuning regime, it is found that the virtual photon exchange can induce a long-range interaction between atoms, which results in correlated excitations. In particular, the atomic blockade phenomenon occurs when the induced long-range interaction effectively suppresses the double atomic excitation, when the average photon number takes certain values, which makes the two nearest energy levels degenerate. We also show that quantum phase transitions occur in the indirectly interacting atomic ensemble when the average photon number reaches several critical points. In this sense, the quantum statistical properties of the collective excitations are very sensitive to the change of the average photon number. Our model exhibits quantum phase transitions similar to the ones in the Lipkin-Meshkov-Glick model. Our proposal could be implemented in a variety of systems including cavity quantum electrodynamics (QED), Bose-Einstein condensates, and circuit QED.
In recent years, the study of quantum electrodynamics (QED) in light-matter interactions has discovered various interesting phenomenons that orient many applications. However, due to the ambient entanglement among photons and atoms, few-particle dynamics remains challenging to analyze precisely and limits the progress in several fields. In few-particle systems, different number of atoms interacting with the light field generates drastically different results, even when there is only a single photon involved in the system. The interference between individual atom’s spontaneous emission wavefunctions can cooperatively alter the effective atom-light coupling strength. Depending on the spatial distance between individual of atoms and the involved cavities in the interaction progresses, the collective spontaneous emission rate can alter drastically from superradiance, where the emission rate is enhanced to a high value proportional to the atom number, to subradiance, where the excited atom ensemble stays in a dark state with the light trapped forever. Superradiance provides a promising mechanism to create an ultra-strong light-matter coupling environment, which is an important ingredient for the design of ultra-fast optical devices, frequency comb generation and quantum mirrors. The dark state of subradiance, on the other hand, is essential for the quantum memory implementation. Also, nontrivial phenomenons also occur when multiple photons interacting with a single atom simultaneously. When a finite number of photons incidents on an atom, their scattering through an atom is highly nonlinear, and one special eigenstate component of such nonlinear process, namely photonic bound states, exhibits many interesting properties in nonlinear quantum optical systems. The photons in such state are strongly bunched with each other, as if a virtual attractive force is in effect. Also, the frequency of photons are anti-correlated so that their total frequency remains a constant value, no matter how arbitrary the frequency of any individual is. Thesefeatures benefit certain nonlinear quantum processes for quantum computing and quantum imaging. Specially for two-photon excitation imaging, the same-parity two-level fluorophore molecules suffers from extremely low excitation efficiencies due to the far off-resonant intermediate states. However, by replacing the current commonly used ultrashort laser pulse illuminations with two photon bound state photon pairs, namely photonic dimers, the efficiency can be enhanced to orders of magnitude higher. Such exceptionally high excitation efficiency can potentially bring the current in vivo deep brain imaging depth from millimeter level to several centimeters. To obtain a stable source of such photonic dimers, it is found that a laser structure with gain medium of two-photon emission materials is capable of generating the coherent state of photonic dimer and can serve as a promising light source for nonlinear quantum optical devices.
Many quantum device signals are proportional to the number of the participating atoms that take part in the detection devices. Among these are optical magnetometers, atomic clocks, quantum communications and atom interferometers. One way to enhance the signal-to-noise ratio is to introduce atom entanglement that increases the signal in a super-radiant-like effect. A coherent em field inside a laser cavity is suggested to achieve atoms’ correlation/entanglement. This may also play an important role in the basic quantum arena of many-body physics. An initial novel experiment to test the realization of atoms’ correlation is described here. A Cs optical magnetometer is used as a tool to test the operation of a cell-in-cavity laser and its characteristics. A vapor cell is inserted into an elongated external cavity of the pump laser in Littrow configuration. Higher atom polarization and reduced laser linewidth are obtained leading to better magnetometer sensitivity and signal-to-noise ratio. The Larmor frequency changes of the Free Induction Decay of optically pumped Cs atomic polarization in the ambient earth magnetic field at room temperature is measured. Temporal changes in the magnetic field of less than 10 pT/√Hz are measured. The first-order dependence of the magnetic field on temperature and temperature gradients is eliminated, important in many practical applications. Single and gradiometric magnetometer configurations are presented.
The resonances between the spontaneous and induced emissions by two- and single photon transitions of three inverted radiators from the ensemble proposed in paper45 open the new possibilities in the manipulation of the decay rate of the entangled photon pairs generated by the system relative the dipole-forbidden transition. The influence of the bath temperature to such process is studied. One of them corresponds to the situation when the total energy of emitted photons by two dipole-active radiators enter the two-photon resonance with the dipoleforbidden transitions of third atom. Second effect corresponds to the scattering situation, when the difference of the excited energies of two dipole-active radiators are in the resonance with the dipole-forbidden transitions of third atom. These effects are accompanied with the interferences between single- and two-quantum collective transitions of three inverted radiators from the ensemble. The three particle collective decay rate is defined in the description of the atomic correlation functions. © (2012) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
New technologies providing tight focusing lens and mirrors with large numerical apertures and electro-optic modulation of single photons are now available for the investigation of photon-atom interactions without a cavity. From the theoretical side, new models must be developed which take into account the intrinsic open system aspect of the problem as well as details about atomic relative positions and temporal (spectral) features of the pulses. In this paper, we investigate the generation of nonclassical correlations between two atoms in response to their interaction with a quantized pulse containing just one single photon. For this purpose, we develop a general theoretical approach which allows us to find the equations of motion for single- and two-body atomic operators from which we obtained the system density operator. We show that one single photon is capable of generating substantial entanglement between the atoms, and we analyze the dependence of these correlations on atomic relative positions and spectral features of the pulse.