Spatial and temporal evolution is studied of two powerful short laser pulses having different wavelengths and interacting with a dense three-level Lambda-type optical medium under coherent population trapping. A general case of unequal oscillator strengths of the transitions is considered. Durations of the probe pulse and the coupling pulse $T_{1,2}$ ($T_2>T_1$) are assumed to be shorter than any of the relevant atomic relaxation times. We propose analytical and numerical solutions of a self-consistent set of coupled Schrödinger equations and reduced wave equations in the adiabatic limit with the account of the first non-adiabatic correction. The adiabaticity criterion is also discussed with the account of the pulse propagation. The dynamics of propagation is found to be strongly dependent on the ratio of the transition oscillator strengths. It is shown that envelopes of the pulses slightly change throughout the medium length at the initial stage of propagation. This distance can be large compared to the one-photon resonant absorption length. Eventually, the probe pulse is completely reemitted into the coupling pulse during propagation. The effect of localization of the atomic coherence has been observed similar to the one predicted by Fleischhauer and Lukin (PRL, {\bf 84}, 5094 (2000).
The stationary light pulse (SLP) refers to a zero-group-velocity optical pulse in an atomic ensemble prepared by two counter-propagating driving fields. Despite the uniqueness of an optical pulse trapped within an atomic medium without a cavity, observations of SLP so far have been limited to trapping a single optical pulse due to the stringent SLP phase-matching condition, and this has severely hindered the development of SLP-based applications. In this paper, we first show theoretically that the SLP process in fact supports two phase-matching conditions and we then utilize the result to expe…
Quantum computing with an inhomogeneously broadened ensemble of ions: Suppression of errors from detuning variations by specially adapted pulses and coherent population trapping
We isolate a novel four-wave mixing process, enabled by Coherent Population Trapping (CPT), leading to efficient phase sensitive amplification. This process is permitted by the exploitation of two transitions starting from the same twofold degenerate ground state. One of the transitions is used for CPT, defining bright and dark states from which ultra intense four-wave mixing is obtained via the other transition. This leads to the measurement of a strong phase sensitive gain even for low optical densities and out-of-resonance excitation. The enhancement of four-wave mixing is interpreted in th…
The phenomenon of Coherent Population Trapping (CPT) of an atom (or solid state "artificial atom"), and the associated effect of Electromagnetically Induced Transparency (EIT), are clear demonstrations of quantum interference due to coherence in multi-level quantum systems. We report observation of CPT in a superconducting phase qubit by simultaneously driving two coherent transitions in a $Λ$-type configuration, utilizing the three lowest lying levels of a local minimum of a phase qubit. We observe $60(\pm 7)%$ suppression of excited state population under conditions of CPT resonance. We pres…
We study phase-dependent fluctuations of the resonance fluorescence of a single $Λ$-type three-level atom in the regime near coherent population trapping, i.e., alongside the two-photon detuning condition. To this end, we employ the method of conditional homodyne detection (CHD) which considers squeezing in the weak driving regime, and extends to non-Gaussian fluctuations for saturating and strong fields. In this framework, and using estimated parameter settings of the resonance fluorescence of a single trapped $^{138} \mathrm{Ba}^{+}$ ion, the light scattered from the probe transitions is fou…
We propose a procedure to achieve a complete energy conversion between laser pulses carrying orbital angular momentum (OAM) in a cloud of cold atoms characterized by a double-Λatom-light coupling scheme. A pair of resonant spatially dependent control fields prepare atoms in a position-dependent coherent population trapping state, while a pair of much weaker vortex probe beams propagate in the coherently driven atomic medium. Using the adiabatic approximation we derive the propagation equations for the probe beams. We consider a situation where the second control field is absent at the entrance…
Efficient photon-photon interaction is one of the key elements for realizing quantum information processing. The interaction, however, must often be mediated through an atomic medium due to the bosonic nature of photons, and the interaction time, which is critically linked to the efficiency, depends on the properties of the atom-photon interaction. While the electromagnetically induced transparency effect does offer the possibility of photonic quantum memory, it does not enhance the interaction time as it fully maps the photonic state to an atomic state. The stationary light pulse (SLP) effect…
Coherent population trapping is a well-known quantum phenomenon in a driven $Λ$ system, with many applications across quantum optics. However, when a stochastic bath is present in addition to vacuum noise, the observed trapping is no longer perfect. Here we derive a time-convolutionless master equation describing the equilibration of the $Λ$ system in the presence of additional temporally correlated classical noise, with an unknown decay parameter. Our simulations show a one-to-one correspondence between the decay parameter and the depth of the characteristic dip in the photoluminescence spect…
We theoretically investigate how population can be trapped in the excited doublet in presence of vacuum-induced coherence (VIC). We employ delayed pulses to transfer population from a metastable state to the excited states. Subsequently, spontaneous emission from the excited doublet builds coherence between them. This coherence can be probed by using chirping, which leads to the decoupling of the excited doublet from the ground state thereby ensuring population transfer via delayed pulses. Our results indicate that the existence of VIC leads to the generation of a mixed state in the excited st…
We studied theoretically a coherent population trapping resonance formation in cylindrical cell without buffer gas irradiated by a narrow laser beam. We take into account non-zero probabilities of elastic ("specular") and inelastic ("sticking") collision between the atom and the cell wall. We have developed a theoretical model based on averaging over the random Ramsey pulse sequences of times that atom spent in and out of the beam. It is shown that the shape of coherent population trapping resonance line depends on the probability of elastic collision.
We consider a three-node fully connected network (Delta network) showing that a coherent population trapping phenomenon occurs, generalizing results for the Lambda network known to support a dark state. Transport in such structures provides signatures of detrapping, which can be triggered by external controls. In the presence of an environment it turns out to be sensitive to its Markovianity. Adiabatic modulation of the system's parameters may yield coherent population transfer, analogous to the stimulated Raman adiabatic passage phenomenon. Robustness of this protocol against non-adiabatic tr…
The coherent population trapping (CPT) effect is used for making compact atomic clocks. There are two types of CPT clocks: the one in which the Raman beams are applied continuously and the one in which two CPT pulses separated by a dark period are applied (Ramsey scheme). It is obvious that the technique of spin squeezing can only be applied to the Ramsey CPT clock to enhance the sensitivity. However, it is not apparent how to adapt to the CPT clock the protocols for the microwave clock using one-axis-twist squeezing (OATS), since the Ramsey CPT clock is not trivially equivalent to the Ramsey …
We present a coherent population trapping based scheme to attain sub-nanoscale resolution for atom localization, microscopy and lithography. Our method uses three-level atoms coupled to amplitude modulated probe field and spatially dependent drive field. The modulation of the probe field allows us to tap into the steep dispersion normally associated with electromagnetically induced transparency and offers an avenue to attain sub-nanometer resolution using just optical fields. We illustrate application of the techniques to the area of microscopy and lithography and show how multilevel schemes o…
A novel protocol of interrogation based on coherent population trapping in an N-level scheme atomic system leads to dark resonances involving three different photons. An ensemble of several hundreds of radiofrequency-trapped ions is probed by three lasers simultaneously locked onto the same optical frequency comb, resulting in high-contrast spectral lines referenced to an atomic transition in the THz domain. We discuss the cause of uncertainties and limitations for this method and show that reaching a sub-kHz resolution is experimentally accessible via this interrogation protocole.
Electromagnetically induced transparency (EIT) is an optical phenomenon which allows a drastic modification of the optical properties of an atomic system by applying a control field. It has been largely studied in the last decades and nowadays we can find a huge number of experimental and theoretical related studies. Recently a similar phenomenon was also shown in quantum dot molecules (QDM) , where the control field is replaced by the tunneling rate between quantum dots. Our results show that in the EIT regime, the optical properties of QDM and the atomic system are identical. However, here w…
Coherent control of quantum systems has far-reaching implications in quantum engineering. In this context, coherent population trapping (CPT) involving dark resonances has played a prominent role, leading to a wealth of major applications including laser cooling of atoms and molecules, optical magnetometry, light storage and highly precise atomic clocks. Extending CPT methods to individual solid-state quantum systems has been only achieved in cryogenic environments for electron spin impurities and superconducting circuits. Here, we demonstrate efficient CPT of a single nuclear spin in a room t…
We have detected and analyzed narrow, high contrast coherent population trapping resonances, which appear in transmission of the probe monochromatic light beam under action of the counterpropagating two-frequency laser radiation, on example of the nonclosed three level Λ-system formed by spectral components of the Doppler broadened D2 line of cesium atoms (in the cell with the rarefied Cs vapor). These nontrivial resonances are determined directly by the trapped atomic population on the definite lower level of the Λ-system and may be used in atomic frequency standards, sensitive magnetometers …
We propose and theoretically analyze the use of coherent population trapping of a single diamond nitrogen vacancy (NV) center for continuous real-time sensing. The formation of the dark state in coherent population trapping prevents optical emissions from the NV center. Fluctuating magnetic fields, however, can kick the NV center out of the dark state, leading to a sequence of single-photon emissions. A time series of the photon counts detected can be used for magnetic field estimations, even when the average photon count per update time interval is much smaller than 1. For a theoretical demon…
Coherent control of two-state systems is traditionally achieved by resonant pulses of specific Rabi frequency and duration, by adiabatic techniques using level crossings or delayed pulses, or by sequences of pulses with precise relative phases (composite pulses). Here we develop a method for high-fidelity coherent control which uses a sequence of detuning pulses. By using the detuning pulse areas as control parameters, and driving on an analogy with composite pulses, we report a great variety of detuning pulse sequences for broadband and narrowband transition probability profiles.
We analyze the properties of a pulsed Coherent Population Trapping protocol that uses a controlled decay from the excited state in a $Λ$-level scheme. We study this problem analytically and numerically and find regimes where narrow transmission, absorption, or fluorescence spectral lines occur. We then look for optimal frequency measurements using these spectral features by computing the Allan deviation in the presence of ground state decoherence and show that the protocol is on a par with Ramsey-CPT. We discuss possible implementations with ensembles of alkali atoms and single ions and demons…
Optical spin rotations and cycling transitions for measurement are normally incompatible in quantum dots, presenting a fundamental problem for quantum information applications. Here we show that for a hole spin this problem can be addressed using a trion with one hole in an excited orbital, where strong spin-orbit interaction tilts the spin. Then, a particular trion triplet forms a double $Λ$ system, even in a Faraday magnetic field, which we use to demonstrate fast hole spin initialization and coherent population trapping. The lowest trion transitions still strongly preserve spin, thus combin…
Magnetically induced coherent population trapping has been studied in a single trapped laser cooled ion. The magnetic field dependent narrow spectral feature is found to be an useful tool in determining the null point of magnetic field at the ion position. In particular, we use a double lambda scheme that allows us to measure the null magnetic field point limited by the detector shot noise. We analyzed the system theoretically and found certain long lived bright states as the dark state is generated under steady state condition.
Hybrid spin-optomechanical quantum systems offer high flexibility, integrability and applicability for quantum science and technology. Particularly, on-chip surface acoustic waves (SAWs) can efficiently drive spin transitions in the ground states (GSs) of atomic-scale, color centre qubits, which are forbidden in case of the more frequently used electromagnetic fields. Here, we demonstrate that strain-induced spin interactions within their optically excited state (ES) can exceed by two orders of magnitude the ones within the GS. This gives rise to novel physical phenomena, such as the acoustica…
Coherent population trapping (CPT) provides a highly sensitive means for probing the energy level structure of an atomic system. For a nitrogen vacancy center in diamond, the CPT offers an alternative to the standard optically-detected magnetic resonance method for measuring the hyperfine structure of the electronic ground states. We show that the nuclear spin dependent CPT measures directly the hyperfine splitting of these states due to the 14N nuclear spin. The CPT spectral response obtained in the presence of a strong microwave field, resonant or nearly resonant with a ground state spin tra…
We report high resolution coherent population trapping on a single hole spin in a semiconductor quantum dot. The absorption dip signifying the formation of a dark state exhibits an atomic physics-like dip width of just 10 MHz. We observe fluctuations in the absolute frequency of the absorption dip, evidence of very slow spin dephasing. We identify this process as charge noise by, first, demonstrating that the hole spin g-factor in this configuration (in-plane magnetic field) is strongly dependent on the vertical electric field, and second, by characterizing the charge noise through its effects…
Quantum interference is a natural consequence of wave-particle duality in quantum mechanics, and is widely observed at the atomic scale. One interesting manifestation of quantum interference is coherent population trapping (CPT), first proposed in three-level driven atomic systems and observed in quantum optical experiments. Here, we demonstrate CPT in a gate-defined semiconductor double quantum dot (DQD), with some unique twists as compared to the atomic systems. Specifically, we observe CPT in both driven and non-driven situations. We further show that CPT in a driven DQD could be used to ge…
Coherent pulse control for quantum memory is viable in the optical domain but nascent in microwave quantum circuits. We show how to realize coherent storage and on-demand pulse retrieval entirely within a superconducting circuit by exploiting and extending existing electromagnetically induced transparency technology in superconducting quantum circuits. Our scheme employs a linear array of superconducting artificial atoms coupled to a microwave transmission line.
The finite-amplitude short coherent control pulse with small random errors in its direction is considered. We derive the conditions for it to approximate an ideal delta-shaped pulse up to an error in the second order of pulse duration. Whether the symmetric and asymmetric pulse shapes would fulfill these conditions is also analyzed. The result shows that, under one of these conditions, all symmetric pulse shapes can fulfill this condition but not for all asymmetric ones..
The total mass of noncollinear photons forming diverging light pulses is defined and found explicitly. Both classical and quantum derivations are presented. The quantum derivation is based on the use of multimode coherent states, and links between parameters of these states and those of the classical field strength are established.
