Exciton Relaxation Research Articles

Ultrafast Exciton and Trion Dynamics in High‐Quality Encapsulated MoS2Monolayers

The extreme confinement and reduced screening in monolayer transition metal dichalcogenides (TMDs) leads to the appearance of tightly bound excitons which can also couple to free charges, forming trions, owing to strong Coulomb interactions. Low temperatures and encapsulation in hexagonal boron nitride (hBN) can narrow the excitonic linewidth, approaching the regime of homogeneous broadening, mostly dominated by the radiative decay. Ultrafast spectroscopy is a perfect tool to study exciton formation and relaxation dynamics in TMD monolayers. However, high‐quality hBN‐encapsulated structures have usually lateral sizes of the order of a few micrometers, calling for the combination of high spatial and temporal resolution in pump–probe experiments. Herein, a custom broadband pump–probe optical microscope is used to measure the ultrafast dynamics of neutral and charged excitons in high‐quality hBN‐encapsulated monolayer MoS2at 8 K. Neutral excitons exhibit a narrow linewidth of 7.5 meV, approaching the homogeneous limit, which is related to the fast recombination time of ≈130 fs measured in pump–probe. Moreover, markedly different dynamics of the trions over the neutral ones are observed. The results provide novel insights on the exciton recombination processes in TMD monolayers, paving the way for exploring the ultrafast behavior of excitons and their many‐body complexes in TMD heterostructures.

Conformation control of triplet state diffusion in platinum containing polyfluorene copolymers

AbstractThe spectral diffusion of singlet and triplet excitons in 9,9‐dioctylfluorene‐based conjugated copolymers is investigated using photoluminescence spectroscopy at both low (5 K) and room temperature (300 K). Inclusion of a N,N‐diphenyl‐4‐(pyridin‐2‐yl)aniline moiety into the polymer backbone allows subsequent cyclometalation with platinum acetylacetonate to increase the spin‐orbit coupling and yield radiative decay from the triplet state. For suitably low fractions (≤5%) of bulky ligand inclusion, cyclometalated or not, the resulting longer sequences of fluorene units are able to adopt the chain‐extended β‐phase conformation. Comparison between the phosphorescence spectral diffusion in glassy‐ and β‐phase Pt‐copolymer samples provide insight into the triplet exciton transfer in more‐ or less‐disordered conjugated polymer films. It is found in the glassy‐phase samples with shorter conjugation lengths that the triplet exciton relaxation becomes frustrated at low temperature due to a freezing out of the thermally activated hops required to move from one conjugated segment to another. In contrast, for films containing β‐phase chain segments, with increased conjugation lengths, this frustration is lifted as more hopping sites remain accessible through intra‐segment motion. This work demonstrates controlled use of changes in molecular conformation to optimize triplet diffusion properties in a member of the widely deployed fluorene‐based conjugated copolymers.

Thickness-Dependent Dark-Bright Exciton Splitting and Phonon Bottleneck in CsPbBr3-Based Nanoplatelets Revealed via Magneto-Optical Spectroscopy.

The optimized exploitation of perovskite nanocrystals and nanoplatelets as highly efficient light sources requires a detailed understanding of the energy spacing within the exciton manifold. Dark exciton states are particularly relevant because they represent a channel that reduces radiative efficiency. Here, we apply large in-plane magnetic fields to brighten optically inactive states of CsPbBr3-based nanoplatelets for the first time. This approach allows us to access the dark states and directly determine the dark-bright splitting, which reaches 22 meV for the thinnest nanoplatelets. The splitting is significantly less for thicker nanoplatelets due to reduced exciton confinement. Additionally, the form of the magneto-PL spectrum suggests that dark and bright state populations are nonthermalized, which is indicative of a phonon bottleneck in the exciton relaxation process.

Synergistic Control of Hot Exciton Relaxation and Exciton–Polaron Dispersion Using a Polaron Retarder for Long Lifetime in Thermally Activated Delayed Fluorescence Organic Light‐Emitting Diodes

AbstractThe operational stability of thermally activated delayed fluorescence (TADF) organic light‐emitting diodes (OLEDs) is an essential property to utilize their efficient triplet harvesting ability and reduce the usage of expensive metal complexes in commercial applications. In this study, a device strategy for extending the device lifetime using the synergistic effects of the hot exciton relaxation and polaron dispersion is demonstrated. By doping a polaron retarder to a conventional TADF‐emitting layer, the lifetime of the blue TADF device is enhanced by 98% at an initial luminance of 1000 cd m−2. Kinetic modeling describing the device degradation indicates that the concurrent contribution via the suppression of exciton and polaron interactions and hot exciton‐related degradation are the origin of the lifetime enhancement. It is demonstrated that the introduction of the polaron retarder finely fits to the ground and that the excited energetic relationship of the host–dopant structure simultaneously improves the operation lifetime and device efficiency without sacrificing other device characteristics.

Ultrafast Charge Transfer and Delayed Recombination in Graphitic-CN/WTe2 van der Waals Heterostructure: A Time Domain Ab Initio Study

In search of an efficient solar energy harvester, we herein performed a time domain density functional study coupled with nonadiabatic molecular dynamics (NAMD) simulation to gain atomistic insight into the charge carrier dynamics of a graphitic carbon nitride (g-CN)-tungsten telluride (WTe2) van der Waals heterostructure. Our NAMD study predicted ultrafast electron (589 fs) and hole-transfer (807 fs) dynamics in g-CN/WTe2 heterostructure and a delayed electron-hole recombination process (2.404 ns) as compared to that of the individual g-CN (3 ps) and WTe2 (0.55 ps) monolayer. The ultrafast charge transfer is due to strong electron-phonon coupling during the charge-transfer process while comparatively weak electron-phonon coupling, sufficient band gap, comparatively lower nonadiabatic coupling (NAC), and fast decoherence time slow down the electron-hole recombination process. The NAMD results of exciton relaxation dynamics are valuable for insightful understanding of charge carrier dynamics and in designing photovoltaic devices based on organic-inorganic 2D van der Waals heterostructures.

Perovskite superlattices with efficient carrier dynamics.

Compared with their three-dimensional (3D) counterparts, low-dimensional metal halide perovskites (2D and quasi-2D; B2An-1MnX3n+1, such as B = R-NH3+, A = HC(NH2)2+, Cs+; M = Pb2+, Sn2+; X = Cl-, Br-, I-) with periodic inorganic-organic structures have shown promising stability and hysteresis-free electrical performance1-6. However, their unique multiple-quantum-well structure limits the device efficiencies because of the grain boundaries and randomlyoriented quantum wells in polycrystals7. In single crystals, the carrier transport through the thickness direction is hindered by the layered insulating organic spacers8. Furthermore, the strong quantum confinement from the organic spacers limits the generation and transport of free carriers9,10. Also, lead-free metal halide perovskites have been developed but their device performance is limited by their low crystallinity and structural instability11. Here we report a low-dimensional metal halide perovskite BA2MAn-1SnnI3n+1 (BA, butylammonium; MA, methylammonium; n = 1, 3, 5) superlattice by chemical epitaxy. The inorganic slabs are aligned vertical to the substrate and interconnected in a criss-cross 2D network parallel to the substrate, leading to efficient carrier transport in three dimensions. A lattice-mismatched substrate compresses the organic spacers, which weakens the quantum confinement. The performance of a superlattice solar cell has been certified under the quasi-steady state, showing a stable 12.36% photoelectric conversion efficiency. Moreover, an intraband exciton relaxation process may have yielded an unusually high open-circuit voltage (VOC).

Nonlinear optical absorption and ultrafast carrier's dynamics of ZrTe2 by Transient Absorption (TA) Spectrometer

The TMDCs (transition metal di-chalcogenides) family provides a platform to discover novel physical phenomena and exotic electronic properties for various device applications. The ultrafast carrier dynamics of the ZrTe2 sample demonstrate that Transient absorption (TA) signals have (electron-hole) constituents and trap carriers. TA variations depend upon carrier properties and photo-excitation due to spatially localized excitations. In the broadband positive signal obtain from ESA (Excited-State Absorption) and the negative signal from GSA (Ground State Absorption). It is seen that ESA is greater as compared to GSA due to fluence-dependent nonlinear absorption (NLA). To study the TA excitons dynamics of ZrTe2, we attribute positive probe bleach (PB) as hot excitons that are situated at higher excitonic states. The TA from power-dependent decay demonstrates that both types of excitons self-trapped excitons (STE) and free excitons (FE) have three processes, relaxation of ST excitons from F excitons, annihilation process between exciton-exciton and relaxation of the ground state from ST excitons states. The variation in exciton annihilation rate gives the exact information about exciton dynamics, which is the key aspect of transient absorption spectroscopy. The free charge carriers are largely localized and move faster compared to the non-localized trapped charge carriers.

Rapidly expanding spin-polarized exciton halo in a two-dimensional halide perovskite at room temperature.

Monitoring of the spatially resolved exciton spin dynamics in two-dimensional semiconductors has revealed the formation of a spatial pattern and long-range transport of the spin-polarized excitons, which holds promise for exciton-based spin-optoelectronic applications. However, the spatial evolution has been restricted to cryogenic temperatures because of the short exciton spin relaxation times at room temperature. Here, we report that two-dimensional halide perovskites can overcome this limitation owing to their relatively long exciton spin relaxation times and substantial exciton-exciton interactions. We demonstrate the emergence of a halo-like spatial profile in spin-polarized exciton population and its ultrafast expansion at room temperature by performing time-resolved Faraday rotation imaging of spin-polarized excitons in two-dimensional perovskite (C4H9NH3)2(CH3NH3)3Pb4I13. Exciton-exciton exchange interactions induce density-dependent nonlinear relaxation and ultrafast transport of exciton spins and give rise to a rapidly expanding halo-like spatial pattern. The density-dependent spatial control suggests the potential of using two-dimensional halide perovskites for spin-optoelectronic applications.

(Invited) Ultrafast Spectroscopy in Semiconductor Nanocrystals: Revealing the Origin of Single Vs Double Emission, of Optical Gain and the Role of Dopants

A wide variety of materials with nanometre dimensions are increasingly explored for photonic applications. Among them, semiconductor nanocrystals (NCs) are very promising for a variety of uses, including light emission devices (LEDs), lasers, detectors, photovoltaic cells, biological labelling and sensing [1]. Key advantage of NCs is the possibility to tailor their optical response by controlling the electronic structure (“wave function engineering”) through the choice of composition, size and shape. Significant and interesting results have been obtained with heterostructured and doped NCs. Beyond single wavelength tuneable band-edge emission, other regimes have been demonstrated such as intragap emission, simultaneous emission on two different wavelengths, amplified spontaneous emission and laser emission.The luminescent properties are governed by exciton decay, which can proceed through radiative or nonradiative pathways, following different routes. The study of exciton dynamics can allow elucidating the processes connected to single or dual emission and to optical gain. This, in turn, can lead to the identification of the functional and structural characteristics that are responsible for these behaviors. Exciton relaxation occurs on picosecond timescales, so ultrafast optical techniques are required to perform these studies.In this talk, we present studies carried out by ultrafast pump-probe spectroscopy technique, with 100-fs time resolution, on CdSe/CdS and PbS/CdS heterostructured NCs, with different geometries (core/shell, dot-in-rod, dot-in-bulk, with sharp or graded interface) [2-6] and CdSeS and CdZnSe doped NCs [7,8]. These NCs are optically active in the visible and near-infrared spectral region, show single and dual colour photoluminescence emission, optical gain, laser emission and intragap emission [2-9]. The analysis of the experimental data allowed us to unravel the decay processes: the initials take place in a few ps, leading to the ultimate emitting state whose lifetime can extend to hundreds of ps to few ns, allowing for efficient luminescence and optical gain.Our data on heterostructures allowed us to clarify the role of the volume and of the shape of the outer component and the effect of the interface [2-4]. We found that dual emission is possible for both thick and thin quantum-confined shells, and for different interfaces. We studied the decoupling of excitons lying in the two different component of the NC (core exciton and shell exciton) and we revealed the evolution of the exciton barrier known as dynamic hole-blockade effect. We showed that these phenomena are strictly connected to dual emission and optical gain and we identified the condition for their maximum efficiency, in term of band alignment and band transitions. Our results provide a comprehensive understanding of the physical phenomena governing dual-emission mechanisms, suppression of Auger recombination, optical gain and laser emission in heterostructured NCs.Experiments on CdZnSe NCs doped with Mn and on CdSeS NCs engineered with sulfur vacancies, enabled us to disclose donor and acceptor localized states in the band gap. We observed the carrier dynamics responsible for intragap emission which is associated to the emergence of a transient Mn3+ state [7], in the first case, and to a donor state below the conduction band introduced by sulfur vacancies [8], in the latter case.In conclusion, the study of the exciton dynamics in different NCs allowed us to elucidate the relation between structural-morphological characteristics (shape, volume, and interface) and unconventional emission capabilities (dual emission and optical gain) in heterostructures and the photophysics of electronic states introduced by doping. This knowledge is very important to control NC functionalities toward new multilevel electronic or photonic schemes and in applications such as lasers [9], photoelectrochemical (PEC) cell [10], white light emission [11], ratiometric sensing [12].[1] P. V. Kamat and G. D. Scholes, J. Phys. Chem. Lett. 7, 584 (2016)[2] G. Sirigu et al., Phys. Rev. B 96, 155303 (2017)[3] V. Pinchetti et al., ACS Nano 10, 6877-6887 (2016)[4] H. Zhao et al., Nanoscale 8, 4217-4226 (2016)[5] M. Zavelani-Rossi et al., Nano Lett. 10, 3142-3150 (2010)[6] R. Krahne et al., Appl. Phys. Lett. 98, 063105 (2011)[7] K. Gahlot et al., ACS Energy Lett. 4, 729−735 (2019)[8] F. Carulli et al., Nano Lett. 21, 6211−6219 (2021)[9] M. Zavelani-Rossi et al., Laser & Photonics Reviews 6, 678-683 (2012)[10] L. Jin et al., Nano Energy 30, 531-541 (2016)[11] S. Sapra et al., Adv. Mater. 19, 569 (2007)[12] J. Liu et al., ACS Photonics, 2479 (2019)

Optical control of exciton spin dynamics in layered metal halide perovskites via polaronic state formation

One of the open challenges of spintronics is to control the spin relaxation mechanisms. Layered metal-halide perovskites are an emerging class of semiconductors which possess a soft crystal lattice that strongly couples electronic and vibrational states and show promise for spintronic applications. Here, we investigate the impact of such strong coupling on the spin relaxation of excitons in the layered perovskite BA2FAPbI7 using a combination of cryogenic Faraday rotation and transient absorption spectroscopy. We report an unexpected increase of the spin lifetime by two orders of magnitude at 77 K under photoexcitation with photon energy in excess of the exciton absorption peak, and thus demonstrate optical control over the dominant spin relaxation mechanism. We attribute this control to strong coupling between excitons and optically excited phonons, which form polaronic states with reduced electron-hole wave function overlap that protect the exciton spin memory. Our insights highlight the special role of exciton-lattice interactions on the spin physics in the layered perovskites and provide a novel opportunity for optical spin control.

Observation of Ultrafast Interfacial Exciton Formation and Relaxation in Graphene/MoS2 Heterostructure.

Heterostructures constructed from graphene and transition metal dichalcogenides (TMDs) have established a new platform for optoelectronic applications. After a large number of studies, one intriguing debate is the existence of the interfacial exciton in graphene/TMDs. Hereby, by combined optical pump-terahertz probe spectroscopy and transient absorption spectroscopy, we report the observation of the interfacial exciton in graphene/MoS2 heterostructure. With the photon energy well below the band gap of monolayer MoS2, the hot electrons of graphene are transferred to MoS2 within 0.5 ps; subsequently, the relaxation of the holes in graphene and electrons in MoS2 shows an identical time scale of 15-18 ps, which manifests the formation and relaxation of the interfacial exciton in the heterostructure following photoexcitation. Moreover, a model of the carrier heating and photogating effect in graphene is proposed to estimate the amount of transferred charge, which agrees well with the experimental results. Our study provides insights into the dynamics of graphene-based heterostructure interfacial non-equilibrium carriers.

Efficient carrier multiplication and extraction in aqueous-processed giant CdTe-CdS nanocrystal bulk heterostructures

Auger recombination as an intrinsic mechanism for bypassing the ‘phonon bottleneck’ plays an important role in semiconductor quantum dots, which makes the possible carrier multiplication or multiple-exciton generation occurred in nanoscale. Here, we show that for aqueous-processed giant CdTe-CdS core-shell nanocrystal solids (the diameter of CdTe core is ∼20 nm, larger than its bulk exciton Bohr radius of ∼7.5 nm), it is a type-II structure with small band offsets and strong delocalization of electrons. Thus, there is an efficient carrier multiplication by Auger processes, in comparison with the exciton relaxation behaviors in reference films consisting of large CdTe quantum dots (the diameter is ∼11 nm) synthesized by an oil-phase approach. The efficient carrier extractions are further demonstrated using TiO2 and MoO3 as carrier transport layers in CdTe-CdS nanocrystal depleted bulk heterostructures, and imbalanced carrier extraction efficiencies by TiO2 and MoO3 are revealed. Our findings unravel the fundamental photophysical mechanisms for the high-efficient all-solid nanocrystal photovoltaics based on aqueous-processed giant CdTe-CdS nanocrystal solids.

Efficient Green Phosphorescent Organic Light Emitting Diode using Iridium Complex

We report here the fabrication and characterization of an efficient green phosphorescent organic light emitting diodes (PhOLED) using phosphorescent iridium complex, tris(2-phenylpyridine) iridium (III) (Ir(ppy)3). Ir(ppy)3 is an organic phosphorescent material, which emits green light via both the singlet as well as triplet exciton relaxation. To avoid triplettriplet annihilation and for efficient light emission, the phosphorescent emitters should be doped in a suitable host material which has band-gap larger than the doped guest material and the band gap of the guest should lie within the band-gap of the host. We optimally doped phosphorescent Ir(ppy)3 into a fluorescent 4,4'-bis(9-carbazolyl) biphenyl (CBP) host and used it as the emitter to prepare PhOLEDs. The PhOLED exhibited green electroluminescence (EL) in the range ~ 480-650 nm with EL peak at 550 nm along with a shoulder at 510 nm. The Commission Internationale de-I’eclairage (CIE) colour coordinate of the device was measured to be (0.25, 0.60). The current density vs voltage vs luminescence (J-V-L) characteristics of the device led us to calculate its current efficiency, which was found to be 28.9 cd/A at 7V. The efficiency of PhOLED decreased with increment in the applied voltage beyond 7 V and has been attributed to the triplet-triplet annihilation due to high injected current densities.

Ab initio calculations of spin-nonconserving exciton–phonon scattering in monolayer transition metal dichalcogenides

We investigate the spin-nonconserving relaxation channel of excitons by their couplings with phonons in two-dimensional transition metal dichalcogenides using ab initio approaches. Combining GW-Bethe–Salpeter equation method and density functional perturbation theory, we calculate the electron–phonon and exciton–phonon coupling matrix elements for the spin-flip scattering in monolayer WSe2, and further analyze the microscopic mechanisms influencing these scattering strengths. We find that phonons could produce effective in-plane magnetic fields which flip spin of excitons, giving rise to relaxation channels complimentary to the spin-conserving relaxation. Finally, we calculate temperature-dependent spin-flip exciton–phonon relaxation times. Our method and analysis can be generalized to study other two-dimensional materials and would stimulate experimental measurements of spin-flip exciton relaxation dynamics.

Imaging the effect of high photoexcited densities on valley polarization and coherence in MoS2 monolayers

We have investigated the laser-induced valley polarization and coherence of encapsulated MoS2 monolayer as a function of temperature, power density, and spatial position. Besides a non-monotonic dependence on temperature, recently attributed to a dependence of the valley relaxation time on the momentum scattering rate, we observe a two-fold increase of the valley polarization when increasing the laser excitation power. We attribute this effect to a local heating induced by the energy relaxation of photoexcited excitons and to an increase of the exciton-exciton scattering rate. In contrast, only a moderate enhancement of valley coherence is observed, which exhibits a dramatic drop after further increasing the excitation power. We attribute this behaviour to the detrimental role of exciton-exciton interactions on the pure dephasing rate responsible for the loss of coherence between the valleys. This manifests itself by a strong dip in the spatial profile of the valley coherence at high photoexcited densities.

Room‐Temperature Observation of Near‐Intrinsic Exciton Linewidth in Monolayer WS2 (Adv. Mater. 15/2022)

Exciton Linewidth Due to strong multiparticle interactions in 2D transition metal dichalcogenides at room temperature, their homogeneous exciton linewidths are significantly broadened, degrading the quality of their excitonic mode and emission. In article number 2108721, Yuebing Zheng and co-workers achieve near-intrinsic exciton linewidth in monolayer WS2 at room temperature, approaching the theoretical limit at 0 K. A dielectric nanosphere is designed to boost the dynamic competition between exciton and trion decay channels, rebuilding the excitonic relaxation processes with suppressed exciton nonradiative recombination.

Vibrational Modes Promoting Exciton Relaxation in the B850 Band of LH2.

Exciton relaxation dynamics in multichromophore systems are often modeled using Redfield theory, where bath fluctuations mediate the relaxation among the exciton eigenstates. Identifying the vibrational or phonon modes that are implicated in exciton relaxation allows more detailed understanding of exciton dynamics. Here we focus on a well-studied light-harvesting II complex (LH2) isolated from the photosynthetic purple bacterium Rhodoblastus acidophilus strain 10050. Using two synchronized mode-locked lasers, we carried out a polarization-dependent two-dimensional electronic spectroscopy (2DES) study of an ultrafast exciton relaxation in the B850 band of LH2. 2DES data with different polarization configurations enable us to investigate the exciton relaxation between the k = ±1 exciton states. Then, we identify vibrational modes coupled to the exciton relaxation by analyzing the coherent wavepackets in the 2DES signals. Focusing on the coherent vibrational wavepackets, the data suggest that certain symmetry-breaking modes of monomeric units play a key role in exciton relaxation.

Regulation of the luminescence mechanism of two-dimensional tin halide perovskites

Two-dimensional (2D) Sn-based perovskites are a kind of non-toxic environment-friendly luminescent material. However, the research on the luminescence mechanism of this type of perovskite is still very controversial, which greatly limits the further improvement and application of the luminescence performance. At present, the focus of controversy is defects and phonon scattering rates. In this work, we combine the organic cation control engineering with temperature-dependent transient absorption spectroscopy to systematically study the interband exciton relaxation pathways in layered A2SnI4 (A = PEA+, BA+, HA+, and OA+) structures. It is revealed that exciton-phonon scattering and exciton-defect scattering have different effects on exciton relaxation. Our study further confirms that the deformation potential scattering by charged defects, not by the non-polar optical phonons, dominates the excitons interband relaxation, which is largely different from the Pb-based perovskites. These results enhance the understanding of the origin of the non-radiative pathway in Sn-based perovskite materials.

Exciton Cooling in 2D Perovskite Nanoplatelets: Rationalized Carrier-Induced Stark and Phonon Bottleneck Effects.

Using femtosecond transient absorption (fs-TA), we investigate the hot exciton relaxation dynamics in strongly confined lead iodide perovskite nanoplatelets (NPLs). The large quantum and dielectric confinement leads to discrete excitonic transitions and strong Stark features in the TA spectra. This prevents the use of conventional relaxation analysis methods extracting the carrier temperature or measuring the buildup of the band-edge bleaching. Instead, we show that the TA spectral line shape near the band-edge reflects the state of the system, which can be used to probe the exciton cooling dynamics. The ultrafast hot exciton relaxation in one- to three- monolayer-thick NPLs confirms the absence of intrinsic phonon bottleneck. However, excitation fluence-dependent measurements reveal a hot phonon bottleneck effect, which is found to be independent of the nature of the internal cations but strongly affected by the ligands and/or sample surface state. Together, these results suggest a role of the surface ligands in the cooling process.

Dynamics of a Nonlinear Quantum Oscillator Under Non-Markovian Pumping

We consider dynamics of a quantum nonlinear oscillator subjected to non-Markovian pumping. Models of this kind can describe formation of exciton-polariton Bose–Einstein condensates in course of stimulated scattering and relaxation of reservoir excitons. Using the Markovian embedding techniques, we obtain stochastic differential equations of motion with an additional degree of freedom corresponding to dynamical memory. We show that the oscillator asymptotically tends to the intrinsically non-Markovian stable fixed point corresponding to constant product of oscillator amplitude and modulo of the memory variable. The state corresponding to this point exhibits unlimited growth of population, with the growth rate that decreases with time. Our results show that the Markovian behavior could be observed only within some limited early stage of the oscillator evolution provided that decay of dynamical memory is sufficiently fast. Transition from the Markovian regime to non-Markovian one with increasing time is linked to the phase shift of the pumping term. We study the coherence properties of the oscillator and find that interaction between particles delimits growth of the condensate population, thereby impeding formation of the Bose–Einstein condensate.